Modeling, Stability, and Control of Dynamic Systems and Their Applications

Journal Name	Impact Factor	CiteScore	Launched Year	First Decision (median)	APC
AppliedMath appliedmath	1.4	1.4	2021	20.4 Days	CHF 1200
Axioms axioms	1.5	-	2012	21.6 Days	CHF 2400
Fractal and Fractional fractalfract	3.5	6.8	2017	17.2 Days	CHF 2700
Mathematics mathematics	2.3	5.4	2013	17.4 Days	CHF 2600
Symmetry symmetry	2.2	5.2	2009	16.3 Days	CHF 2400

24 pages, 772 KB

Open AccessArticle

Global Stability and Bifurcation of a Three-Species Commensalism–Amensalism Model with Beddington–DeAngelis Functional Response

by Xiaoran Li, Qin Yue and Fengde Chen

Axioms 2026, 15(7), 495; https://doi.org/10.3390/axioms15070495 - 1 Jul 2026

Viewed by 165

Abstract

This paper investigates the dynamical behavior of a three-species commensalism–amensalism system with Beddington–DeAngelis functional response. The model describes a novel tripartite interaction: a neutral–commensal species (e.g., sea anemone) simultaneously engages in a commensal relationship with a commensal–amensal species (e.g., clownfish) and an indirect [...] Read more.

This paper investigates the dynamical behavior of a three-species commensalism–amensalism system with Beddington–DeAngelis functional response. The model describes a novel tripartite interaction: a neutral–commensal species (e.g., sea anemone) simultaneously engages in a commensal relationship with a commensal–amensal species (e.g., clownfish) and an indirect nutritional coupling with a neutral–amensal species (e.g., crustacean), while the commensal–amensal and neutral–amensal species interact amensalistically. This paper makes three principal contributions. First, by constructing a Volterra-type Lyapunov function, we rigorously prove the global asymptotic stability of the unique positive equilibrium of the

(x, z)

-subsystem in the positive quadrant, and further establish the global asymptotic stability of both the amensal-free equilibrium

E_{3}

and the coexistence equilibrium

E_{4}

in the positive octant. Second, selecting the commensal benefit coefficient c as the bifurcation parameter, we present a complete and rigorous proof of a transcritical bifurcation. Third, we provide systematic Maple-based numerical verification: the bifurcation diagram exhibits excellent agreement with the theoretical curve, and logarithmic-scale plots confirm exponential convergence rates. Ecologically, our results reveal a sharp threshold phenomenon: when the commensal benefit coefficient lies below a critical value

c^{*}

, the commensal species inevitably goes extinct and the system collapses to a two-species state; when c exceeds

c^{*}

, the commensal species can invade and achieve stable three-species coexistence. The explicit formula for this threshold provides a quantitative criterion for determining the minimum mutualistic strength required for persistence in conservation contexts. The results obtained in this paper substantially extend the existing theoretical understanding of three-species commensalism–amensalism systems. Full article

(This article belongs to the Topic Modeling, Stability, and Control of Dynamic Systems and Their Applications)

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28 pages, 8945 KB

Open AccessArticle

Artificial Neural Network (ANN)-Based Analysis and Optimal Control of Smoking Dynamics with Global Sensitivity Assessment

by Ines Ben Omrane, Naeem Ullah, Ghaliah Alhamzi and Mohammadi Begum Jeelani

Fractal Fract. 2026, 10(6), 409; https://doi.org/10.3390/fractalfract10060409 - 16 Jun 2026

Viewed by 346

Abstract

The main objective of this study is to investigate smoking dynamics, identify the most influential factors governing smoking behavior, and develop effective intervention strategies through the integration of fractional-order modeling, sensitivity analysis, optimal control theory, and artificial neural networks (ANNs). A nonlinear fractional-order [...] Read more.

The main objective of this study is to investigate smoking dynamics, identify the most influential factors governing smoking behavior, and develop effective intervention strategies through the integration of fractional-order modeling, sensitivity analysis, optimal control theory, and artificial neural networks (ANNs). A nonlinear fractional-order compartmental model is formulated by dividing the population into potential smokers, light smokers, heavy smokers, and quit smokers. The smoking reproduction number is derived to characterize the transmission and persistence of smoking behavior within the population. To determine the impact of model parameters on smoking dynamics, both normalized forward sensitivity analysis and global sensitivity analysis based on Latin Hypercube Sampling (LHS) with Partial Rank Correlation Coefficient (PRCC) are performed. The obtained results identify the most sensitive transmission and progression parameters and demonstrate their important role in shaping smoking prevalence within the community. Furthermore, the classical integer-order model is compared with the fractional-order formulation, where the fractional model provides a more realistic description due to its ability to incorporate memory and hereditary effects associated with smoking behavior. An optimal control framework involving awareness and treatment strategies is further introduced to investigate effective smoking reduction policies. The numerical results demonstrate that awareness campaigns reduce smoking initiation, while treatment interventions increase smoking cessation, and the combined implementation of both strategies produces the most significant reduction in smoking prevalence. The consistency between the sensitivity analysis and optimal control results further supports the reliability of the proposed framework. Numerical simulations are carried out to analyze the qualitative and quantitative behavior of the system under different epidemiological scenarios. In addition, an ANN-based computational framework is employed as an efficient numerical tool to accurately approximate the complex dynamics of the proposed fractional-order smoking model with very low prediction error. Overall, the present study provides a comprehensive mathematical and computational framework for understanding, analyzing, and controlling smoking behavior within a population. Full article

(This article belongs to the Topic Modeling, Stability, and Control of Dynamic Systems and Their Applications)

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15 pages, 227 KB

Open AccessArticle

An Algorithm with Remote Set Control for Inverse Strongly Monotone Mappings

by Alexander J. Zaslavski

Mathematics 2026, 14(11), 1838; https://doi.org/10.3390/math14111838 - 25 May 2026

Viewed by 248

Abstract

In 2003, W. Takahashi and M. Toyoda established the weak convergence of the iteration process of solving a variational inequality problem. This variational inequality is associated with an inverse strongly monotone mapping. In our recent research, we showed that most of the exact [...] Read more.

In 2003, W. Takahashi and M. Toyoda established the weak convergence of the iteration process of solving a variational inequality problem. This variational inequality is associated with an inverse strongly monotone mapping. In our recent research, we showed that most of the exact iterates of the same iterative process are approximate solutions of the variational inequality. In this paper, we apply a method with remote set control in order to find a common solution of a family of variational inequality problems, generated by inverse strongly monotone mappings, and a family of fixed point problems, which are not necessarily finite, in the presence of computational errors. Our results are obtained under the presence of summable and nonsummable computational errors. Full article

(This article belongs to the Topic Modeling, Stability, and Control of Dynamic Systems and Their Applications)

26 pages, 4301 KB

Open AccessArticle

TD3-Based Reinforcement Learning for Adaptive PID-like Control of Uncertain Dynamical Systems

by Ufuk Demircioğlu, Halit Bakır, Badar Almarri and A. H. Abdul Hafez

Mathematics 2026, 14(10), 1744; https://doi.org/10.3390/math14101744 - 19 May 2026

Viewed by 342

Abstract

This paper presents a TD3-based reinforcement learning framework for adaptive PID-like control of uncertain dynamical systems. Although proportional–integral–derivative (PID) control remains widely used because of its simplicity, interpretability, and practical effectiveness, fixed-gain PID controllers often experience performance degradation in the presence of external [...] Read more.

This paper presents a TD3-based reinforcement learning framework for adaptive PID-like control of uncertain dynamical systems. Although proportional–integral–derivative (PID) control remains widely used because of its simplicity, interpretability, and practical effectiveness, fixed-gain PID controllers often experience performance degradation in the presence of external disturbances, parameter variations, and changing operating conditions. To address this limitation, the control task is formulated as a continuous-action reinforcement learning problem in which the observation vector is constructed from PID-related error components, namely the tracking error, its integral, and its derivative. Based on these error-derived observations, a Twin Delayed Deep Deterministic Policy Gradient (TD3) agent learns a bounded continuous control policy through interaction with the environment while preserving a PID-like structural interpretation. The proposed framework is evaluated on a representative mass–spring–damper system under three challenging scenarios: external disturbance, parametric uncertainty, and their simultaneous presence. Its performance is further examined for both constant-reference regulation and sinusoidal reference tracking. The simulation results show that the learned controller achieves stable and accurate tracking, fast transient response, and robust behavior across varying operating conditions. These findings demonstrate the potential of TD3-based reinforcement learning as an effective adaptive PID-like control strategy for uncertain dynamical systems. Full article

(This article belongs to the Topic Modeling, Stability, and Control of Dynamic Systems and Their Applications)

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40 pages, 12987 KB

Open AccessArticle

Topological Digital Twins: A Reduced-Order Framework for the Analysis and Forecasting of Convective Systems

by Hélène Canot, Philippe Durand and Emmanuel Frenod

Mathematics 2026, 14(9), 1513; https://doi.org/10.3390/math14091513 - 30 Apr 2026

Viewed by 434

Abstract

We propose an exploratory framework based on Topological Digital Twins (TDTs) for the monitoring and short-term forecasting of spatial dynamical systems. The approach represents the system through a reduced state built from topological descriptors obtained via persistent homology. These descriptors capture features such [...] Read more.

We propose an exploratory framework based on Topological Digital Twins (TDTs) for the monitoring and short-term forecasting of spatial dynamical systems. The approach represents the system through a reduced state built from topological descriptors obtained via persistent homology. These descriptors capture features such as connected components, cycles, and large-scale structure. The framework combines three components: an observation operator mapping spatial fields to a low-dimensional state, a reduced dynamical model evolving this state in time, and a data assimilation step aimed at improving robustness. This construction maps persistence diagrams to a finite-dimensional Euclidean space. This makes the model tractable but does not preserve the full algebraic structure of the original topological objects. We provide theoretical results supporting the stability of the representation under perturbations of the input field. The method is illustrated on a bow-echo convective system observed over Corsica on 18 August 2022, where the reduced state captures the main structural organization of the system over time. A comparison with standard nowcasting methods shows complementary behavior: pixel-based approaches provide better local accuracy, while the TDT framework better preserves the global spatial structure, as reflected by Wasserstein distances and persistence-based comparisons. Additional tests also indicate that the topological observables remain stable under small perturbations of the input field. The present study is based on a single case and should be understood as a proof of concept, rather than as a definitive validation. Future work will focus on validation on larger datasets and on the use of more advanced dynamical models. Full article

(This article belongs to the Topic Modeling, Stability, and Control of Dynamic Systems and Their Applications)

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25 pages, 10606 KB

Open AccessArticle

A ZMP-Aware Task Formulation for Reference-Driven Humanoid Tracking in MuJoCo MPC

by Shaoshuai Xu, Yan Wang and Zhixun Su

Symmetry 2026, 18(5), 768; https://doi.org/10.3390/sym18050768 - 29 Apr 2026

Viewed by 506

Abstract

Reference-driven humanoid motion tracking aims to reproduce a source motion on a target humanoid while preserving physical executability under actuation limits and changing contact conditions. The problem becomes particularly challenging for dynamic motions involving rapid support transitions, landing impacts, mixed hand–foot contacts, and [...] Read more.

Reference-driven humanoid motion tracking aims to reproduce a source motion on a target humanoid while preserving physical executability under actuation limits and changing contact conditions. The problem becomes particularly challenging for dynamic motions involving rapid support transitions, landing impacts, mixed hand–foot contacts, and moderate topology-preserving morphology variation. Existing pipelines often rely heavily on morphology-specific world-frame targets or treat balance and contact quality only indirectly during execution, which limits their reliability under dynamic contact variation. This paper presents a task and cost formulation for reference-driven humanoid tracking within the residual-based MuJoCo model predictive control (MPC) framework. The source motion is decomposed into a pelvis-centered canonical local reference, pelvis height and tilt references, and a pelvis-derived horizontal center-of-mass (CoM) velocity intent, and is tracked online with a zero moment point (ZMP)-aware contact-conditioned residual design including slip, penetration, posture, and control regularization. The formulation is compatible with standard MuJoCo MPC planners, and the evaluation is conducted under a shared iterative linear quadratic Gaussian (iLQG) setting on nominal and morphology-varied humanoids against tracking-only and two-stage inverse-kinematics (IK)-based baselines. The proposed formulation improves success rate, support quality, slip reduction, and progression accuracy, with the clearest gains on contact-sensitive motions; for example, success rate increases from 56.7% to 76.7% on Jump–Turn and from 46.7% to 70.0% on Cartwheel relative to the tracking-only MPC baseline. These results support the use of execution-oriented reference representation and contact-conditioned residual design for physically reliable reference-driven humanoid tracking. Full article

(This article belongs to the Topic Modeling, Stability, and Control of Dynamic Systems and Their Applications)

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26 pages, 659 KB

Open AccessArticle

Stability and Direction of Hopf Bifurcation with Optimal Control Analysis of HIV Transmission Dynamics

by Ibraheem M. Alsulami and Fahad Al Basir

Mathematics 2026, 14(6), 1079; https://doi.org/10.3390/math14061079 - 23 Mar 2026

Viewed by 581

Abstract

In this study, we examine the effectiveness of combining interleukin-2 (IL-2) with highly active antiretroviral therapy (HAART) in controlling HIV replication. A mathematical model of the immune system is developed to analyze immune recovery when IL-2 is administered alongside HAART. We investigate the [...] Read more.

In this study, we examine the effectiveness of combining interleukin-2 (IL-2) with highly active antiretroviral therapy (HAART) in controlling HIV replication. A mathematical model of the immune system is developed to analyze immune recovery when IL-2 is administered alongside HAART. We investigate the stability of the endemic equilibrium and Hopf bifurcation and determine the direction and stability of periodic solutions using center manifold theory. Numerical simulations are conducted to support the theoretical findings. The results show that the disease-free equilibrium is stable when the basic reproduction number

R_{0} < 1

, while the endemic equilibrium exists when

R_{0} > 1

. Our results also reveal the presence of a subcritical Hopf bifurcation in the system. An optimal control problem is also studied, showing that the combined therapy of IL-2 and HAART improves treatment outcomes, reduces side effects, and has a unique optimal control pair. Sensitivity analysis further highlights the importance of system parameters in influencing treatment effectiveness. Full article

(This article belongs to the Topic Modeling, Stability, and Control of Dynamic Systems and Their Applications)

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21 pages, 739 KB

Open AccessArticle

Feedback Control Design for Time-Delay Systems Based on the Manabe Polynomial Concept Under Unmodeled Input Delay

by Stefan Brock

AppliedMath 2026, 6(3), 51; https://doi.org/10.3390/appliedmath6030051 - 19 Mar 2026

Cited by 2 | Viewed by 575

Abstract

Time delays are inherent in modern motion-control and electric-drive loops due to sensing, filtering, sampling and computation, communication, and actuation scheduling. When such delays are only partially known, they can markedly reduce stability margins and narrow the admissible range of state-feedback gains, especially [...] Read more.

Time delays are inherent in modern motion-control and electric-drive loops due to sensing, filtering, sampling and computation, communication, and actuation scheduling. When such delays are only partially known, they can markedly reduce stability margins and narrow the admissible range of state-feedback gains, especially in high-bandwidth servo applications. This paper develops a design-oriented state-feedback framework for delay-affected plants based on the Manabe polynomial concept and the Coefficient Diagram Method (CDM). The plant is represented as a chain of integrators of order two to four with an effective input gain, and the feedback gain is synthesized for the nominal delay-free model by matching a standard Manabe/CDM characteristic polynomial using the classical CDM stability-index pattern. When an unmodeled input delay is present, the closed loop is governed by a delay-dependent characteristic equation. By introducing a normalized representation, the analysis yields explicit delay-stability limits that directly translate into a lower bound on the equivalent time constant used for tuning. The degradation of the phase margin and gain margin with increasing normalized delay is quantified as design charts, and a simple phase-margin-based inequality is proposed for selecting the tuning time constant, with gain-margin checks recommended as a verification step. Full article

(This article belongs to the Topic Modeling, Stability, and Control of Dynamic Systems and Their Applications)

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21 pages, 2286 KB

Open AccessArticle

Command-Filtered Fuzzy Adaptive Output Feedback Control for Nonlinear Power Systems with Actuator Faults

by Sen Wang, Junzhe Yan, Chenxuan Sheng, Huai Liu and Guobao Liu

Axioms 2026, 15(3), 212; https://doi.org/10.3390/axioms15030212 - 12 Mar 2026

Viewed by 575

Abstract

This study presents a command-filtered fuzzy adaptive control method for nonlinear thyristor controlled series compensation (TCSC) systems subject to actuator faults, unknown nonlinearities, and unmeasurable states. To enhance applicability, the TCSC-based single-machine infinite-bus (SMIB) system is first transformed into a nonlinear form preserving [...] Read more.

This study presents a command-filtered fuzzy adaptive control method for nonlinear thyristor controlled series compensation (TCSC) systems subject to actuator faults, unknown nonlinearities, and unmeasurable states. To enhance applicability, the TCSC-based single-machine infinite-bus (SMIB) system is first transformed into a nonlinear form preserving the inherent nonlinear characteristics of the power system. A state observer is then designed to estimate the unmeasurable states. Using these estimated states, a fuzzy control algorithm approximates the uncertain nonlinearities. By integrating command filtering techniques, an adaptive output feedback controller is developed, which ensures system stability and avoids the “explosion of complexity” issue. Simulation results verify the effectiveness of the proposed control approach. Full article

(This article belongs to the Topic Modeling, Stability, and Control of Dynamic Systems and Their Applications)

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15 pages, 5952 KB

Open AccessArticle

Analysis of Numerical Simulation for Nonlinear Robot Control Based on Dynamic Modeling Using Low-Cost and Open-Source Technology

by Felipe J. Torres, Israel Martínez, Antonio J. Balvantín and Edgar H. Robles

AppliedMath 2026, 6(3), 41; https://doi.org/10.3390/appliedmath6030041 - 5 Mar 2026

Viewed by 587

Abstract

Professors, students, and researchers from universities around the world use software distributed under licenses for numerical simulation purposes, which requires a computer with considerable hardware capabilities. This implies a high cost of simulations in engineering applications that require dynamic modeling using numerical methods, [...] Read more.

Professors, students, and researchers from universities around the world use software distributed under licenses for numerical simulation purposes, which requires a computer with considerable hardware capabilities. This implies a high cost of simulations in engineering applications that require dynamic modeling using numerical methods, particularly in robotics and nonlinear control. This article compares and analyzes the performance of a frugal simulation scheme based on the use of low-cost, free, and open-source technology, specifically a low-power, single-board minicomputer (Raspberry Pi) in conjunction with GNU-Octave software. The benchmark is a numerical simulation of trajectory tracking control in the joint space of a Selective Conformal Assembly Robot Arm (SCARA). To perform this task, a system of coupled nonlinear differential equations is solved in matrix form using a numerical method known as an ODE solver. This solution includes the control law and the dynamic system model derived from Euler–Lagrange formalism. The time complexity and accuracy are analyzed to compare the performance of the frugal simulation tool with that of a conventional simulation setup consisting of a personal computer and MATLAB^TM running the same simulation code. The analysis shows minimal deviations in the numerical solutions and reasonable time complexity. Moreover, the frugality score of this approach and the low acquisition cost of the simulation tool enable the creation of simulation laboratories at universities with limited budgets for education and research. Full article

(This article belongs to the Topic Modeling, Stability, and Control of Dynamic Systems and Their Applications)

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14 pages, 1393 KB

Open AccessArticle

Periodic Event-Triggered Consensus Relying on Previous Information in Leader-Following Multi-Agent Systems

by Huanzhen Wang, Aiping Wang and Miaomiao Wu

Symmetry 2026, 18(2), 271; https://doi.org/10.3390/sym18020271 - 31 Jan 2026

Viewed by 527

Abstract

In this paper, we consider the consensus of leader-following multi-agent systems. We extend a window-based periodic event-triggered strategy to leader-following multi-agent systems. This strategy was originally proposed by Seidel et al. for leaderless consensus. We give an upper bound on the evolution of [...] Read more.

In this paper, we consider the consensus of leader-following multi-agent systems. We extend a window-based periodic event-triggered strategy to leader-following multi-agent systems. This strategy was originally proposed by Seidel et al. for leaderless consensus. We give an upper bound on the evolution of the Lyapunov function and present the consensus condition for our considered leader-following system. This is accomplished by adding the previous information to the general triggering conditions and allowing an increase in the Lyapunov function within a local range as long as a decreasing tendency is still guaranteed. Finally, some simulation examples are given to demonstrate that the proposed approach ensures system consensus while reducing the communication costs. Full article

(This article belongs to the Topic Modeling, Stability, and Control of Dynamic Systems and Their Applications)

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20 pages, 937 KB

Open AccessArticle

Quasi-Consensus of Fractional-Order Multi-Agent Systems with Mixed Delays and External Disturbance via Impulsive Pinning Control

by Tao Chen, Zhiwen Fu, Caimao Su, Ning Chen and Wanli Lin

Fractal Fract. 2026, 10(1), 48; https://doi.org/10.3390/fractalfract10010048 - 12 Jan 2026

Viewed by 769

Abstract

In this brief, the quasi-consensus issue is examined for fractional-order multi-agent systems (FROMASs) subject to both mixed delays and external disturbances, employing an impulsive pinning control (IPC) strategy. Unlike mainstream pinning strategies with fixed nodes or static rules, a dynamic pinning mechanism based [...] Read more.

In this brief, the quasi-consensus issue is examined for fractional-order multi-agent systems (FROMASs) subject to both mixed delays and external disturbances, employing an impulsive pinning control (IPC) strategy. Unlike mainstream pinning strategies with fixed nodes or static rules, a dynamic pinning mechanism based on consensus error distances is proposed, which adaptively adjusts the set of pinned nodes at each impulsive instant. By integrating the Razumikhin method, Lyapunov stability theory, and the comparison system approach, sufficient conditions for achieving quasi-consensus of FROMASs are established. Moreover, the convergence bound of consensus errors is quantitatively estimated and shown to be explicitly determined by the intensity of external disturbances. This paper organically integrates the dynamic node pinning mechanism, FRO impulsive control, and Razumikhin stability analysis. It effectively handles mixed delays and external disturbances while significantly reducing control costs. Finally, numerical simulations show that the synchronization errors are strictly bounded within the threshold

M = 13.6372

, which effectively validates both the proposed control scheme and the theoretical analysis. Full article

(This article belongs to the Topic Modeling, Stability, and Control of Dynamic Systems and Their Applications)

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43 pages, 5402 KB

Open AccessArticle

Dual Nonlinear Saturation Control of Electromagnetic Suspension (EMS) System in Maglev Trains

by Hany Samih Bauomy Abdelmonem

Mathematics 2026, 14(1), 62; https://doi.org/10.3390/math14010062 - 24 Dec 2025

Cited by 3 | Viewed by 1060

Abstract

This paper presents a nonlinear vertical dynamic model of an electromagnetic suspension (EMS) system in maglev trains regulated by a dual nonlinear saturation controller (DNSC) under simultaneous resonance (

Ω ≅ ω_{s}, ω_{s} ≅ 2 ω_{c}

). [...] Read more.

This paper presents a nonlinear vertical dynamic model of an electromagnetic suspension (EMS) system in maglev trains regulated by a dual nonlinear saturation controller (DNSC) under simultaneous resonance (

Ω ≅ ω_{s}, ω_{s} ≅ 2 ω_{c}

). The governing nonlinear differential equations of the system are addressed analytically utilizing the multiple time-scale technique (MTST), concentrating on resonance situations obtained from first-order approximations. The suggested controller incorporates two nonlinear saturation functions in the feedback and feedforward paths to improve system stability, decrease vibration levels, and enhance passenger comfort amidst external disturbances and parameter changes. The dynamic bifurcations caused by DNSC parameters are examined through phase portraits and time history diagrams. The goal of control is to minimize vibration amplitude through the implementation of a dual nonlinear saturation control law based on displacement and velocity feedback signals. A comparative analysis is performed on different controllers such as integral resonance control (IRC), positive position feedback (PPF), nonlinear integrated PPF (NIPPF), proportional integral derivative (PID), and DNSC to determine the best approach for vibration reduction in maglev trains. DNSC serves as an effective control approach designed to minimize vibrations and enhance the stability of suspension systems in maglev trains. Stability evaluation under concurrent resonance is conducted utilizing the Routh–Hurwitz criterion. MATLAB 18.2 numerical simulations (fourth-order Runge–Kutta) are employed to analyze time-history responses, the effects of system parameters, and the performance of controllers. The evaluation of all the derived solutions was conducted to verify the findings. Additionally, quadratic velocity feedback leads to intricate bifurcation dynamics. In the time domain, higher displacement and quadratic velocity feedback may destabilize the system, leading to shifts between periodic and chaotic movements. These results emphasize the substantial impact of DNSC on the dynamic performance of electromagnetic suspension systems. Frequency response, bifurcation, and time-domain evaluations demonstrate that the DNSC successfully reduces nonlinear oscillations and chaotic dynamics in the EMS system while attaining enhanced transient performance and resilience. Full article

(This article belongs to the Topic Modeling, Stability, and Control of Dynamic Systems and Their Applications)

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18 pages, 458 KB

Open AccessArticle

Mathematical Modeling of Canine and Human Rabies

by Abdramane Annour Saad and Mahamat Saleh Daoussa Haggar

AppliedMath 2025, 5(4), 182; https://doi.org/10.3390/appliedmath5040182 - 17 Dec 2025

Cited by 1 | Viewed by 976

Abstract

This article presents a deterministic model describing the joint dynamics of canine and human rabies in a cross-border context. This model explicitly integrates dog mobility between two neighboring countries and allows us to assess the impact of these movements on disease persistence. We [...] Read more.

This article presents a deterministic model describing the joint dynamics of canine and human rabies in a cross-border context. This model explicitly integrates dog mobility between two neighboring countries and allows us to assess the impact of these movements on disease persistence. We analyze the basic reproduction number

R_{0}

, study the local and global stability of equilibrium points, identify the most influential parameters through sensitivity analysis, and perform numerical simulations to test the effectiveness of different vaccination and movement control strategies. Full article

(This article belongs to the Topic Modeling, Stability, and Control of Dynamic Systems and Their Applications)

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23 pages, 351 KB

Open AccessArticle

Solvability of a Coupled System of Hadamard Fractional p-Laplacian Differential Equations with Infinite-Point Boundary Conditions at Resonance on an Unbounded Interval

by Yao Lu, Wei Zhang and Quanxin Zhu

Fractal Fract. 2025, 9(11), 688; https://doi.org/10.3390/fractalfract9110688 - 27 Oct 2025

Cited by 2 | Viewed by 1091

Abstract

This paper investigates a coupled system of Hadamard fractional p-Laplacian differential equations defined on an unbounded interval, subject to infinitely many points boundary conditions and formulated under a resonance framework. Under suitable growth assumptions imposed on the nonlinear terms of the system, [...] Read more.

This paper investigates a coupled system of Hadamard fractional p-Laplacian differential equations defined on an unbounded interval, subject to infinitely many points boundary conditions and formulated under a resonance framework. Under suitable growth assumptions imposed on the nonlinear terms of the system, the existence of solutions is established by means of the Ge–Mawhin’s continuation theorem. Moreover, an example is constructed to demonstrate the applicability of the main results. Full article

(This article belongs to the Topic Modeling, Stability, and Control of Dynamic Systems and Their Applications)

16 pages, 3995 KB

Open AccessArticle

An Explicit Positivity-Preserving Method for Nonlinear Aït-Sahalia Model Driven by Fractional Brownian Motion

by Zhuoqi Liu

Symmetry 2025, 17(10), 1649; https://doi.org/10.3390/sym17101649 - 4 Oct 2025

Viewed by 837

Abstract

This paper develops an explicit positivity-preserving method for the nonlinear Aït-Sahalia interest rate model driven by fractional Brownian motion. To overcome the difficulties in obtaining the convergence rate of this positivity-preserving method, the Lamperti transformation is utilized, which gives an auxiliary equation. And [...] Read more.

This paper develops an explicit positivity-preserving method for the nonlinear Aït-Sahalia interest rate model driven by fractional Brownian motion. To overcome the difficulties in obtaining the convergence rate of this positivity-preserving method, the Lamperti transformation is utilized, which gives an auxiliary equation. And the convergence rate of the numerical method for this auxiliary equation is obtained by virtue of Malliavin calculus. Naturally, the target follows from the inverse of the Lamperti transformation. As a byproduct, the convergence rate of the explicit positivity-preserving method for stochastic differential equations driven by fractional Brownian motion with symmetric coefficients is obtained. Finally, several numerical experiments are performed to verify the theoretical results and demonstrate the advantage of the explicit method. Full article

(This article belongs to the Topic Modeling, Stability, and Control of Dynamic Systems and Their Applications)

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60 pages, 1430 KB

Open AccessArticle

The Effect of the Cost Functional on Asymptotic Solution to One Class of Zero-Sum Linear-Quadratic Cheap Control Differential Games

by Valery Y. Glizer and Vladimir Turetsky

Symmetry 2025, 17(9), 1394; https://doi.org/10.3390/sym17091394 - 26 Aug 2025

Viewed by 946

Abstract

A finite-horizon zero-sum linear-quadratic differential game with non-homogeneous dynamics is considered. The key feature of this game is as follows. The cost of the control of the minimizing player (the minimizer) in the game’s cost functional is much smaller than the cost of [...] Read more.

A finite-horizon zero-sum linear-quadratic differential game with non-homogeneous dynamics is considered. The key feature of this game is as follows. The cost of the control of the minimizing player (the minimizer) in the game’s cost functional is much smaller than the cost of the control of the maximizing player (the maximizer) and the cost of the state variable. This smallness is due to a positive small multiplier (a small parameter) for the quadratic form of the minimizer’s control in the integrand of the cost functional. Two cases of the game’s cost functional are studied: (i) the current state cost in the integrand of the cost functional is a positive definite quadratic form; (ii) the current state cost in the integrand of the cost functional is a positive semi-definite (but non-zero) quadratic form. The latter case has not yet been considered in the literature devoted to the analysis of cheap control differential games. For each of the aforementioned cases, an asymptotic approximation (by the small parameter) of the solution to the considered game is derived. It is established that the property of the aforementioned state cost (positive definiteness/positive semi-definiteness) has an essential effect on the asymptotic analysis and solution of the differential equations (Riccati-type, linear, and trivial), appearing in the solvability conditions of the considered game. The cases (i) and (ii) require considerably different approaches to the derivation of the asymptotic solutions to these differential equations. Moreover, the case (ii) requires developing a significantly novel approach. The asymptotic solutions of the aforementioned differential equations considerably differ from each other in cases (i) and (ii). This difference yields essentially different asymptotic solutions (saddle point and value) of the considered game in these cases, meaning it is of crucial importance to distinguish cases (i) and (ii) in the study of various theoretical and real-life cheap control zero-sum linear-quadratic differential games. The asymptotic solutions of the considered game in cases (i) and (ii) are compared with each other. An academic illustrative example is presented. Full article

(This article belongs to the Topic Modeling, Stability, and Control of Dynamic Systems and Their Applications)

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30 pages, 2186 KB

Open AccessArticle

Dynamic Analysis of a Fractional-Order SINPR Rumor Propagation Model with Emotional Mechanisms

by Yuze Li, Ying Liu and Jianke Zhang

Fractal Fract. 2025, 9(8), 546; https://doi.org/10.3390/fractalfract9080546 - 19 Aug 2025

Cited by 3 | Viewed by 1486

Abstract

The inherent randomness and concealment of rumors in social networks exacerbate their spread, leading to significant societal instability. To explore the mechanisms of rumor propagation for more effective control and mitigation of harm, we propose a novel fractional-order Susceptible-Infected-Negative-Positive-Removed (SINPR) rumor propagation model, [...] Read more.

The inherent randomness and concealment of rumors in social networks exacerbate their spread, leading to significant societal instability. To explore the mechanisms of rumor propagation for more effective control and mitigation of harm, we propose a novel fractional-order Susceptible-Infected-Negative-Positive-Removed (SINPR) rumor propagation model, which simultaneously incorporates emotional mechanisms by distinguishing between positive and negative emotion spreaders, as well as memory effects through fractional-order derivatives. The proposed model extends traditional frameworks by jointly capturing the bidirectional influence of emotions and the anomalous, history-dependent dynamics often overlooked by integer-order models. First, we calculate the equilibrium points and thresholds of the model, and analyze the stability of the equilibrium, along with the sensitivity and transcritical bifurcation associated with the basic reproduction number. Next, we validate the theoretical results through numerical simulations and analyze the individual effects of fractional-order derivatives and emotional mechanisms. Finally, we predict the rumor propagation process using real datasets. Comparative experiments with other models demonstrate that the fractional-order SINPR model achieves R-squared values of 0.9712 and 0.9801 on two different real datasets, underscoring its effectiveness in predicting trends in rumor propagation. Full article

(This article belongs to the Topic Modeling, Stability, and Control of Dynamic Systems and Their Applications)

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25 pages, 6900 KB

Open AccessArticle

Detection of Trends and Anomalies with MACD and RSI Market Indicators for Temperature and Precipitation

by Yunus Ziya Kaya

Symmetry 2025, 17(8), 1268; https://doi.org/10.3390/sym17081268 - 8 Aug 2025

Cited by 1 | Viewed by 2052

Abstract

The changes in climatological variables are a critical concern for climatologists, hydrologists, and water resources managers. In the face of global climate change, a more profound understanding of the recent changes in climatological conditions of a specific region is becoming increasingly urgent. To [...] Read more.

The changes in climatological variables are a critical concern for climatologists, hydrologists, and water resources managers. In the face of global climate change, a more profound understanding of the recent changes in climatological conditions of a specific region is becoming increasingly urgent. To this end, hydro-climatological time series are being investigated in various ways, from traditional approaches to state-of-the-art techniques. This manuscript investigates the trend changes of surface temperature and total precipitation hydro-climatological parameters over a long period, using two of the most popular market price trend detection indicators, MACD and RSI. The RSI indicator evaluation methodology has been modified for the hydro-climatological time series. Minimum, maximum, mean surface temperatures, and precipitation parameters were analyzed. The length of the data sets is 122 years, starting in 1901 and ending in 2022. The application of these indicators to the mentioned parameters underscores their potential as powerful tools in the detection of climatological trends and trend variability over time, highlighting the need for proactive climate management strategies. The results revealed that the MACD and RSI indicators are effective tools not only for trend detection but also for determining climatological anomalies. These tools can be used to complement traditional statistical trend analysis. Moreover, their visual capabilities allow the methods to offer a more comprehensive understanding of climate management strategies. Full article

(This article belongs to the Topic Modeling, Stability, and Control of Dynamic Systems and Their Applications)

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22 pages, 3715 KB

Open AccessArticle

Fractional-Order Creep Hysteresis Modeling of Dielectric Elastomer Actuator and Its Implicit Inverse Adaptive Control

by Yue Wang, Yuan Liu, Xiuyu Zhang, Xuefei Zhang, Lincheng Han and Zhiwei Li

Fractal Fract. 2025, 9(8), 479; https://doi.org/10.3390/fractalfract9080479 - 22 Jul 2025

Viewed by 1251

Abstract

Focusing on the dielectric elastomer actuator (DEA), this paper proposes a backstepping implicit inverse adaptive control scheme with creep direct inverse compensation. Firstly, a novel fractional-order creep Krasnoselskii–Pokrovskii (FCKP) model is established, which effectively captures hysteresis behavior and creep dynamic characteristics. Significantly, this [...] Read more.

Focusing on the dielectric elastomer actuator (DEA), this paper proposes a backstepping implicit inverse adaptive control scheme with creep direct inverse compensation. Firstly, a novel fractional-order creep Krasnoselskii–Pokrovskii (FCKP) model is established, which effectively captures hysteresis behavior and creep dynamic characteristics. Significantly, this study pioneers the incorporation of the fractional-order method into a hysteresis-coupled creep model. Secondly, based on the FCKP model, the creep direct inverse compensation is developed to combine with the backstepping implicit inverse adaptive control scheme, where the implicit inverse algorithm avoids the construction of the direct inverse model to mitigate hysteresis. Finally, the proposed control scheme was validated on the DEA system control experimental platform. Under both single-frequency and composite-frequency conditions, it achieved mean absolute errors of 0.0035 and 0.0111, and root mean square errors of 0.0044 and 0.0133, respectively, demonstrating superior tracking performance compared to other control schemes. Full article

(This article belongs to the Topic Modeling, Stability, and Control of Dynamic Systems and Their Applications)

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20 pages, 317 KB

Open AccessArticle

Linking Controllability to the Sturm–Liouville Problem in Ordinary Time-Varying Second-Order Differential Equations

by Manuel De la Sen

AppliedMath 2025, 5(3), 87; https://doi.org/10.3390/appliedmath5030087 - 8 Jul 2025

Viewed by 935

Abstract

This paper establishes some links between Sturm–Liouville problems and the well-known controllability property in linear dynamic systems, together with a control law design that allows any prefixed arbitrary final state finite value to be reached via feedback from any given finite initial conditions. [...] Read more.

This paper establishes some links between Sturm–Liouville problems and the well-known controllability property in linear dynamic systems, together with a control law design that allows any prefixed arbitrary final state finite value to be reached via feedback from any given finite initial conditions. The scheduled second-order dynamic systems are equivalent to the stated second-order differential equations, and they are used for analysis purposes. In the first study, a control law is synthesized for a forced time-invariant nominal version of the current time-varying one so that their respective two-point boundary values are coincident. Afterward, the parameter that fixes the set of eigenvalues of the Sturm–Liouville system is replaced by a time-varying parameter that is a control function to be synthesized without performing, in this case, any comparison with a nominal time-invariant version of the system. Such a control law is designed in such a way that, for given arbitrary and finite initial conditions of the differential system, prescribed final conditions along a time interval of finite length are matched by the state trajectory solution. As a result, the solution of the dynamic system, and thus that of its differential equation counterpart, is subject to prefixed two-point boundary values at the initial and at the final time instants of the time interval of finite length under study. Also, some algebraic constraints between the eigenvalues of the Sturm–Liouville system and their evolution operators are formulated later on. Those constraints are based on the fact that the solutions corresponding to each of the eigenvalues match the same two-point boundary values. Full article

(This article belongs to the Topic Modeling, Stability, and Control of Dynamic Systems and Their Applications)

17 pages, 3066 KB

Open AccessArticle

Multiple UAV Cooperative Substation Inspection: A Robust Fixed-Time Group Formation Control Scheme

by Lirong Xiao, Zhongwei Xiao, Zheng Fu, Cheng Cheng, Fan Li and Yang Yang

Symmetry 2025, 17(6), 857; https://doi.org/10.3390/sym17060857 - 31 May 2025

Cited by 1 | Viewed by 1099

Abstract

This study investigates the cooperative substation inspection problem for multi-unmanned aerial vehicle systems (MUAVs) subjected to uncertain disturbances. To enhance inspection reliability and efficiency, a novel distributed fixed-time group consensus control scheme is proposed. In this framework, radial basis function neural networks (RBF [...] Read more.

This study investigates the cooperative substation inspection problem for multi-unmanned aerial vehicle systems (MUAVs) subjected to uncertain disturbances. To enhance inspection reliability and efficiency, a novel distributed fixed-time group consensus control scheme is proposed. In this framework, radial basis function neural networks (RBF NNs) are employed to approximate both intrinsic nonlinear uncertainties and uncertain disturbances affecting UAV dynamics. Subsequently, a distributed fixed-time controller is developed via backstepping techniques, where fixed-time command filters are integrated to circumvent the complexity explosion inherent to conventional backstepping. Furthermore, an approximation error compensation system is established. It mitigates estimation inaccuracies arising from RBF NN approximations and command filtering processes. The mathematical analysis demonstrates that the proposed controller ensures the fixed-time convergence of group consensus errors into an adjustable residual set. Finally, numerical simulations and MUAV group formation simulations validate the robustness against aerodynamic uncertainties. Full article

(This article belongs to the Topic Modeling, Stability, and Control of Dynamic Systems and Their Applications)

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19 pages, 440 KB

Open AccessArticle

Finite-Time Synchronization and Practical Synchronization for Caputo Fractional-Order Fuzzy Cellular Neural Networks with Transmission Delays and Uncertainties via Information Feedback

by Hongguang Fan, Hui Wen, Kaibo Shi and Anran Zhou

Fractal Fract. 2025, 9(5), 297; https://doi.org/10.3390/fractalfract9050297 - 2 May 2025

Cited by 4 | Viewed by 1370

Abstract

This article considers a class of Caputo fractional-order fuzzy cellular neural networks (CFOFCNNs) with transmission delays and uncertain perturbations. In particular, nonlinear activations and fuzzy operators AND and OR are investigated in the drive-response neural networks (NNs). To achieve practical finite-time (PFT) synchronization [...] Read more.

This article considers a class of Caputo fractional-order fuzzy cellular neural networks (CFOFCNNs) with transmission delays and uncertain perturbations. In particular, nonlinear activations and fuzzy operators AND and OR are investigated in the drive-response neural networks (NNs). To achieve practical finite-time (PFT) synchronization and finite-time (FT) synchronization of the studied systems, we design new nonlinear controllers including four feedback terms in this paper, and each carries a different role in the control process. Integrating different comparison principles and nonlinear feedback schemes, straightforward synchronization criteria of the CFOFCNNs are derived. Unlike existing works, a significant finding is that adjusting the feedback coefficients and parameters can enable synchronization switching. Namely, changing one of the feedback terms from positive to negative can cause PFT synchronization to switch to FT synchronization via adjusted control parameters, making our control methods applicable to different scenarios. The settling time depends explicitly on feedback coefficients, initial conditions, and fractional order. Full article

(This article belongs to the Topic Modeling, Stability, and Control of Dynamic Systems and Their Applications)

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24 pages, 16861 KB

Open AccessArticle

Modeling a Multi-Lane Highway System Considering the Combined Impacts of Overtaking Mechanisms and Aggressive Lane-Changing Behaviors

by Shuhong Yang, Bin Huang, Chuan Tian and Yirong Kang

Mathematics 2025, 13(8), 1291; https://doi.org/10.3390/math13081291 - 15 Apr 2025

Cited by 4 | Viewed by 1851

Abstract

This paper suggests a new multi-lane lattice model that incorporates both overtaking mechanisms and drivers’ aggressive lane-changing behaviors to investigate macroscopic traffic stability in multi-lane expressway environments. To enhance the fidelity of lane-changing simulation, the proposed model reformulates lane-changing protocols by integrating empirical [...] Read more.

This paper suggests a new multi-lane lattice model that incorporates both overtaking mechanisms and drivers’ aggressive lane-changing behaviors to investigate macroscopic traffic stability in multi-lane expressway environments. To enhance the fidelity of lane-changing simulation, the proposed model reformulates lane-changing protocols by integrating empirical observations of aggressive driving patterns in real-world scenarios. Through theoretical derivation, we formulate a density wave partial differential equation that captures the spatio-temporal propagation of congestion patterns near critical stability thresholds while analytically obtaining the linear stability criterion for the proposed model. The validity of these theoretical constructs is validated through systematic numerical simulation. Key findings reveal that when overtaking passing rates are relatively low, the driver’s aggressive lane-changing strategy exhibits a pronounced stabilizing effect on multi-lane systems and effectively mitigates traffic oscillation amplitudes. Conversely, under high passing rate conditions, such aggressive driving behaviors are shown to exert detrimental effects on both traffic fluctuation suppression and system-wide stability. Notably, our findings also demonstrate that expanding the number of lanes merges as a viable strategy to enhance systemic robustness. Full article

(This article belongs to the Topic Modeling, Stability, and Control of Dynamic Systems and Their Applications)

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11 pages, 1301 KB

Open AccessArticle

Analyzing the Transient Process and the Realizability of Fractional Systems via Intermittent Control

by Jianbing Hu, Chuteng Ying, Shuguang Li, Zhe Jin, Xiaochao Chao and Xia Wang

Fractal Fract. 2025, 9(3), 184; https://doi.org/10.3390/fractalfract9030184 - 16 Mar 2025

Cited by 3 | Viewed by 945

Abstract

In this paper, we have studied the transient process and the realizability of fractional systems via intermittent control. For any system under intermittent control input, a transient oscillation process is inevitable when the input switches, which is irrelevant to mathematical model. But this [...] Read more.

In this paper, we have studied the transient process and the realizability of fractional systems via intermittent control. For any system under intermittent control input, a transient oscillation process is inevitable when the input switches, which is irrelevant to mathematical model. But this process is usually neglected when considering the achievements of fractional intermittent control systems as the initial value is changed by the switching input. The obtained theoretical results cannot agree with the real physical model. The input signal is treated as a piecewise signal by means of convolution operation and unit step function, and the output is drawn by convoluting the control input with a time decay function. We have drawn the conclusions that the initial value of the fractional model can not be updated by any outer input and that a transient process must exist that is related to all historic process and the memory property of a fractional system. If the response function of a system is taken as the time decay function, the results obtained are in good agreement with the actual model and can be used to analyze the transient phenomena in nature. Some examples are presented to verify our theoretical achievements. Full article

(This article belongs to the Topic Modeling, Stability, and Control of Dynamic Systems and Their Applications)

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15 pages, 435 KB

Open AccessArticle

Verification of Detectability for Time Labeled Petri Net Systems with Unobservable Transitions

by Tao Qin and Zhiwu Li

Mathematics 2025, 13(4), 563; https://doi.org/10.3390/math13040563 - 8 Feb 2025

Cited by 1 | Viewed by 1576

Abstract

We investigate the detectability verification problem of time-dependent systems modeled by time labeled Petri nets that are a typical time-dependent model of many computer-integrated systems in modern society, characterized by networked connections. In a time labeled Petri net, the detectability proposed in this [...] Read more.

We investigate the detectability verification problem of time-dependent systems modeled by time labeled Petri nets that are a typical time-dependent model of many computer-integrated systems in modern society, characterized by networked connections. In a time labeled Petri net, the detectability proposed in this paper characterizes the current state of a time-dependent system that can be uniquely determined after a finite number of observations within a given time instant. Moreover, we further define strong and weak detectability in a time labeled Petri net system. To verify strong and weak detectability, we excogitate a label-based state class graph, which is not required to enumerate all states of a system, to compute the states for a given real-time observation. Based on the proposed label-based state class graph, an information structure called a timed state observer is formulated to verify strong and weak detectability. The proposed verification technique is advantageous and is effectively applied to an intelligent garage system, since the enumeration of all states of the time-dependent system is not required. Full article

(This article belongs to the Topic Modeling, Stability, and Control of Dynamic Systems and Their Applications)

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22 pages, 9285 KB

Open AccessArticle

A Control Method for Thermal Structural Tests of Hypersonic Missile Aerodynamic Heating

by Chao Lu, Guangming Zhang and Xiaodong Lv

Mathematics 2025, 13(3), 380; https://doi.org/10.3390/math13030380 - 24 Jan 2025

Viewed by 2160

Abstract

This paper presents an intelligent proportional-derivative adaptive global nonsingular fast-terminal sliding-mode control (IPDAGNFTSMC) for tracking temperature trajectories of a hypersonic missile in thermal structural tests. Firstly, the numerical analyses on a hypersonic missile’s aerodynamic heating are based on three different external flow fields [...] Read more.

This paper presents an intelligent proportional-derivative adaptive global nonsingular fast-terminal sliding-mode control (IPDAGNFTSMC) for tracking temperature trajectories of a hypersonic missile in thermal structural tests. Firstly, the numerical analyses on a hypersonic missile’s aerodynamic heating are based on three different external flow fields via the finite element calculation, which provides the data basis for the thermal structural test of hypersonic vehicles; secondly, due to temperature trajectory differences of a hypersonic missile and the thermal inertia and nonlinear characteristics of quartz lamps in thermal structural test, IPDAGNFTSMC is proposed, consisting of three components: (i) the mathematical model of the thermal structural test is established and further replaced via an intelligent proportional-derivative with a nonlinear extended state observer (NESO) for online unknown disturbances observation; (ii) compared with the traditional sliding-mode control method, the AGNFTSMC method eliminates the reaching phase and the initial control state is trapped on the sliding-mode surface. Therefore, it can alleviate chattering phenomenon, accelerate the convergence rate of the sliding mode, and ensure that there is no singular problem in the entire control process; (iii) the adaptive law is designed to effectively solve problems of convergence stagnation and chattering phenomenon. The Lyapunov stability theory is used to prove the stability of the proposed IPDAGNFTSMC-NESO. Finally, the advantages of the designed control method are verified by experimental simulation and comparison. Full article

(This article belongs to the Topic Modeling, Stability, and Control of Dynamic Systems and Their Applications)

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18 pages, 2009 KB

Open AccessArticle

Convergence Rates of Partial Truncated Numerical Algorithm for Stochastic Age-Dependent Cooperative Lotka–Volterra System

by Mengqing Zhang, Quanxin Zhu and Jing Tian

Symmetry 2024, 16(12), 1659; https://doi.org/10.3390/sym16121659 - 15 Dec 2024

Cited by 1 | Viewed by 1343

Abstract

We present a numerical algorithm for a stochastic age-dependent cooperative Lotka–Volterra system that incorporates a partially truncated function. Since it is challenging to obtain the real solution for this system, and traditional numerical algorithms often experience blow-up phenomena, we design a partially truncated [...] Read more.

We present a numerical algorithm for a stochastic age-dependent cooperative Lotka–Volterra system that incorporates a partially truncated function. Since it is challenging to obtain the real solution for this system, and traditional numerical algorithms often experience blow-up phenomena, we design a partially truncated algorithm to ensure the solution remains well behaved. We further establish the convergence of the algorithm and obtain its convergence order. Finally, numerical simulations are presented to demonstrate our theoretical findings. Full article

(This article belongs to the Topic Modeling, Stability, and Control of Dynamic Systems and Their Applications)

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24 pages, 7397 KB

Open AccessArticle

Solution of Fractional Differential Boundary Value Problems with Arbitrary Values of Derivative Orders for Time Series Analysis

by Dmitry Zhukov, Vadim Zhmud, Konstantin Otradnov and Vladimir Kalinin

Mathematics 2024, 12(24), 3905; https://doi.org/10.3390/math12243905 - 11 Dec 2024

Viewed by 1476

Abstract

The paper considers the solution of a fractional differential boundary value problem, that is, a diffusion-type equation with arbitrary values of the derivative orders on an infinite axis. The difference between the obtained results and other authors’ ones is that these involve arbitrary [...] Read more.

The paper considers the solution of a fractional differential boundary value problem, that is, a diffusion-type equation with arbitrary values of the derivative orders on an infinite axis. The difference between the obtained results and other authors’ ones is that these involve arbitrary values of the derivative orders. The solutions described in the literature, as a rule, are considered in the case when the fractional time derivative β lies in the range: 0 < β ≤ 1, and the fractional state derivative α (the variable describing the state of the process) is in the range: 1 < α ≤ 2. The solution presented in the article allows us to consider any ranges for α and β, if the inequality 0 < β/α ≤ 0.865 is satisfied in the range β/α. In order to solve the boundary value problem, the probability density function of the observed state x of a certain process (for example, the magnitude of the deviation of the levels of a time series) from time t (for example, the time interval for calculating the amplitudes of the deviation of the levels of a time series) can be captured. Full article

(This article belongs to the Topic Modeling, Stability, and Control of Dynamic Systems and Their Applications)

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23 pages, 11122 KB

Open AccessArticle

Numerical Investigation of Water Transport and Effective Electrical Conductivity in Perforation of Gas Diffusion Layer Using Lattice Boltzmann Method

by Jae Yong Cho, Hee Min Lee, Muhammad Nasir Bashir and Joon Sang Lee

Fractal Fract. 2024, 8(12), 719; https://doi.org/10.3390/fractalfract8120719 - 5 Dec 2024

Cited by 2 | Viewed by 2297

Abstract

In polymer electrolyte membrane fuel cells, the gas diffusion layer (GDL) is composed of porous media and serves a critical role as a mass transport layer, facilitating reactant gas diffusion, removal of water generated in the catalyst layer, and electron transport. Artificial spacings [...] Read more.

In polymer electrolyte membrane fuel cells, the gas diffusion layer (GDL) is composed of porous media and serves a critical role as a mass transport layer, facilitating reactant gas diffusion, removal of water generated in the catalyst layer, and electron transport. Artificial spacings known as perforations can be introduced to improve water management within this mass transport system. However, the impact of these perforations on the effective electrical conductivity has not been adequately studied. This study employs numerical methods to investigate water management and effective electrical conductivity in the presence of perforations, aiming to provide indicators for optimal design. The pseudopotential lattice Boltzmann method is utilized, which is particularly advantageous for modeling two-phase flow and electron transport in complex geometries. Using this numerical approach, we analyze water penetration in GDL structures and effective electrical conductivity based on electric potential fields focusing on geometric parameters such as the perforation size. Our results demonstrate a relationship between water management efficiency and effective electrical conductivity, suggesting the existence of an optimal perforation diameter. Moreover, when there is a water-induced penetration pattern due to the perforated structure, both the effective electrical conductivity and water management are enhanced at a lower porosity of the GDL structure. Full article

(This article belongs to the Topic Modeling, Stability, and Control of Dynamic Systems and Their Applications)

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