Search Results (282)

The stability of energy demand–supply systems is often affected by delayed feedback caused by regulatory inertia, communication lags, and heterogeneous agent responses. Conventional models typically assume discrete delays, which may oversimplify real dynamics and reduce controller effectiveness. This work addresses this limitation by introducing a novel class of nonlinear energy models with distributed delay feedback governed by gamma-distributed memory kernels. Specifically, we consider both weak (exponential) and strong (Erlang-type) kernels to capture a spectrum of memory effects. Using the linear chain trick, we reformulate the resulting integro-differential model into a higher-dimensional system of ordinary differential equations. Analytical conditions for local asymptotic stability and Hopf bifurcation are derived, complemented by Lyapunov-based global stability criteria. The related numerical analysis confirms the theoretical findings and reveals a distinct stabilization regime. Compared to fixed-delay approaches, the proposed framework offers improved flexibility and robustness, with implications for delay-aware energy control and infrastructure design. Full article

A nonlocal transport–reaction system is proposed to model the coupled dynamics of stem and differentiated cell populations, structured by a continuous damage variable. The framework incorporates bidirectional transitions via differentiation and dedifferentiation, with nonlocal birth operators encoding damage redistribution upon division and Hill-type feedback regulation dependent on total populations. Global well-posedness of solutions in $C([0,\infty );L^1([0,\infty )\times L^1\left([0,\infty )\right))$ is established by combining the contraction mapping principle for local existence with a priori $L^1$ bounds for global existence, ensuring uniqueness and nonnegativity. Integration yields balance laws for total populations, reducing to a finite-dimensional autonomous ordinary differential equation (ODE) system under constant death rates. Linearization reveals a bifurcation threshold separating extinction, homeostasis, and unbounded growth. Under compensatory feedback, Dulac’s criterion precludes periodic orbits, and the Poincaré–Bendixson theorem confines bounded trajectories to equilibria or heteroclinics. Uniqueness implies global asymptotic stability. A scaling invariance for steady states under uniform feedback rescaling is identified. The analysis extends structured population theory to feedback-regulated compartments with nonlocal operators and reversible dedifferentiation, providing explicit stability criteria and linking an infinite-dimensional structured model to tractable low-dimensional reductions. Full article

This paper presents a robust and reliable voltage regulation method in DC–DC converters, for which a multiloop control strategy is developed and analyzed for a boost converter. The proposed control scheme consists of an inner current loop and an outer voltage loop, both systematically designed using the control Lyapunov function (CLF) methodology. The main contributions of this work are (1) the formulation of a control structure capable of maintaining performance under variations in load, reference voltage, and input voltage; (2) the theoretical demonstration of global asymptotic stability of the closed-loop system in the Lyapunov sense; and (3) the experimental validation of the proposed controller on a physical DC–DC boost converter, confirming its effectiveness. The results support the advancement of high-efficiency nonlinear control methods for power electronics applications. Furthermore, the experimental findings reinforce the practical relevance and real-world applicability of the proposed approach. Full article

This research examines the Lyapunov-based criterion for global asymptotic stability of Bidirectional Associative Memory (BAM) neural networks that have mixed-interval time-varying delays. Using a second-order reciprocally convex approach, this paper introduces a novel stability criterion for BAM neural networks with time delays. The literature has recently incorporated a few triple integral expressions in the Lyapunov–Krasovskii functional to lessen conservatism in the analysis of system stability with interval time-varying delays using a second-order reciprocally convex combination strategy. This research work establishes the negative definiteness of the Lyapunov–Krasovskii functional derivative and is formulated using Linear Matrix Inequalities (LMIs). The effectiveness of the proposed result is demonstrated through numerical examples. Full article

We study a stochastic differential model for the dynamics of institutional corruption, extending a deterministic three-variable system—corruption perception, proportion of sanctioned acts, and policy laxity—by incorporating Gaussian perturbations into key parameters. We prove global existence and uniqueness of solutions in the physically relevant domain, and we analyze the linearization around the asymptotically stable equilibrium of the deterministic system. Explicit mean square bounds for the linearized process are derived in terms of the spectral properties of a symmetric matrix, providing insight into the temporal validity of the linear approximation. To investigate global behavior, we relate the first exit time from the domain of interest to backward Kolmogorov equations and numerically solve the associated elliptic and parabolic PDEs with FreeFEM, obtaining estimates of expectations and survival probabilities. An application to the case of Mexico highlights nontrivial effects: while the spectral structure governs local stability, institutional volatility can non-monotonically accelerate global exit, showing that highly reactive interventions without effective sanctions increase uncertainty. Policy implications and possible extensions are discussed. Full article

A spatiotemporal transmission epidemic model is proposed based on human mobility, spatial factors of population migration across multiple regions, individual protection, and government quarantine measures. First, the model’s basic reproduction number and disease-free equilibrium are derived, and the relationship between the basic reproduction number in a single region and that across multiple regions is explored. Second, the global asymptotic stability of both the disease-free equilibrium and the endemic equilibrium is proved by constructing a Lyapunov function. The impact of population migration on the spread of the virus is revealed by numerical simulations, and the global sensitivity of the model parameters is analyzed for a single region. Finally, a protection isolation strategy based on the optimal path is proposed. The experimental results indicate that increasing the isolation rate, improving the treatment rate, enhancing personal protection, and reducing the infection rate can effectively prevent and control the spread of the epidemic. Population migration accelerates the spread of the virus from high-infected areas to low-infected areas, aggravating the epidemic situation. However, effective public health measures in low-infected areas can prevent transmission and reduce the basic reproduction number. Furthermore, if the inflow migration rate exceeds the outflow rate, the number of infected individuals in the region increases. Full article

In the severe context of global warming and the energy crisis, the low-carbon economy has become an inevitable trend in global development. This paper focuses on the logistics industry, a significant domain of carbon emissions, and regards the promotion of new energy logistics vehicles as a crucial breakthrough for the industry to achieve energy savings and emission reductions. From the perspective of an evolutionary game involving the government, logistics vehicle enterprises, and logistics enterprises, a practical and feasible strategy for promoting new energy logistics vehicles is proposed. Firstly, a tripartite evolutionary game model was developed under the dual-credit policy and auxiliary policies, and its strategy of asymptotic stability and Jacobian matrix analysis was conducted. Then, system dynamics (SD) was employed to simulate the model, aiming to explore the impact of key decision variables on the evolutionary outcomes. The results show that: (1) Appropriate auxiliary policy support can encourage logistics vehicle enterprises to produce new energy logistics vehicles and promote the transformation of the logistics industry to a low-carbon direction; (2) Through the optimization of the dual-credit policy and the enhancement of the value of points trading, logistics enterprises can be motivated to produce more new energy vehicles; (3) The promotion of cost reduction of new energy logistics vehicles and the enhancing of market competitiveness can improve the willingness of logistics enterprises to use new energy logistics vehicles; (4) The government should encourage logistics enterprises to use new energy logistics vehicles in multiple dimensions. Full article

The epidemic modeling of computer virus propagation is identified as an effective approach to understanding the mechanism of virus spread. Fraction-order virus spread models exhibit remarkable advantages over their integer-order counterparts. Based on a type of bursting virus, a fractional computer virus propagation model with saturation effect is suggested. The basic properties of the model are discussed. The basic reproduction number of the model is determined. The virus–endemic equilibria of the model are determined. A criterion for the global asymptotic stability of the virus-free equilibrium is derived. For a pair of potential virus–endemic equilibria, criteria for the local asymptotic stability are presented. Some interesting properties of the model, ranging from the impact of the fractional order and the saturation index on virus spread to their coupling effect, are revealed through numerical simulations. This work helps gain a deep insight into the laws governing virus propagation. Full article

Cervical cancer (CC), which continues to be a major public health concern that causes cancer deaths among women worldwide, is mostly caused by persistent human papillomavirus (HPV) infection. This study suggests a dual-delay model of HPV-C infection dynamics that takes into account both cancerous delay and the immune response delay. We identify disease-free and diseased equilibria, investigate their local asymptotic stability, and show that the system is non-negative and bounded. We prove the global asymptotic stability of the equilibria by building Lyapunov functions and using the basic reproduction number $R_0$, and look into the existence of Hopf bifurcations. Additionally, we use forward sensitivity analysis to determine important control parameters. Lastly, the theoretical results were confirmed by numerical simulations. The study demonstrates that time delays play a crucial role in viral transmission and carcinogenesis. The process from HPV infection to the formation of cervical cancer is more correctly simulated by this model, which offers a theoretical mathematical basis for researching the pathophysiology of cervical cancer and developing clinical prevention and control measures. Full article

To address the problems of insufficient trajectory tracking accuracy, pronounced jitter over undulating terrain, and limited disturbance rejection in orchard mobile robots, this paper proposes a trajectory tracking control strategy based on a double-loop adaptive sliding mode. Firstly, a kinematic model of the orchard robot is constructed and a time-varying integral terminal sliding surface is designed to achieve global fast finite-time convergence. Secondly, a sinusoidal saturation switching function with a variable boundary is employed to suppress the high-frequency chattering inherent in sliding mode control. Thirdly, an improved double-power reaching law (Improved DPRL) is introduced to enhance disturbance rejection in the inner loop while ensuring continuity of the outer-loop output. Finally, Lyapunov stability theory is used to prove the asymptotic stability of the double-loop system. The experimental results show that attitude angle error settles within 0.01 rad after 0.144 s, while the position errors in both the x-axis and y-axis directions settle within 0.01 m after 0.966 s and 0.753 s, respectively. Regarding position error convergence, the Integral of Absolute Error (IAE)/Integral of Squared Error (ISE)/Integral of Time-Weighted Absolute Error (ITAE) are 0.7629 m, 0.7698 m, and 0.2754 m, respectively; for the attitude angle error, the IAE/ISE/ITAE are 0.0484 rad, 0.0229 rad, and 0.1545 rad, respectively. These results indicate faster convergence of both position and attitude errors, smoother control inputs, and markedly reduced chattering. Overall, the findings satisfy the real-time and accuracy requirements of fast trajectory tracking for orchard mobile robots. Full article

The widespread application of multi-agent robotic systems in domains such as agricultural collaboration and automation has accentuated the challenges faced in seeking to achieve rapid synchronization and sustain high-performance control under conditions where velocity states remain unmeasurable. To relieve these challenges, a synchronization control framework is proposed for multi-agent systems, employing non-uniform sampling communication protocols. Initially, a state-variable transformation is applied to construct a composite Lyapunov function that integrates a sampling term. An explicit relation is then derived between the communication interval and the global exponential synchronization rate, thereby establishing a theoretical foundation for the design of non-periodic sampling-based control strategies. Second, a linear-state feedback controller is introduced, which balances convergence speed with the limited frequency of information updates, ensuring asymptotic stability even under prolonged sampling intervals. Third, a velocity observer was designed based on Immersion and Invariance ($I\&I$) theory to solve the problem of unmeasurable velocity states, ensuring the exponential convergence of the estimation error. Finally, the simulation results demonstrate that, with sampling intervals of $h\in [0.03,0.08]$ s, the position errors $\parallel q_i-q_{d,i}\parallel$ of all six robots converge to below ${10}^{-2}$ within 7 s; meanwhile, the velocity estimation errors decay to nearly zero within 7 s, confirming the effectiveness of the proposed method. The main contributions of this work can be summarized as follows: (1) a new $I\&I$ velocity observer is tailored for discrete-time communication; (2) rigorous proof of global exponential convergence is provided via a composite Lyapunov energy function; (3) a reproducible MATLAB simulation framework is presented that enhances both the verifiability and applicability of the proposed approach. Full article

This study proposes a novel egg-crate honeycomb core sandwich panel (SP-EHC) that combines the structural advantages of conventional lattice and grid configurations while mitigating their limitations in stability and mechanical performance. The design employs chamfered intersecting grid walls to create a semi-enclosed honeycomb architecture, enhancing out-of-plane stiffness and buckling resistance and enabling ventilation and drainage. To facilitate efficient and accurate structural analysis, a two-dimensional equivalent plate model (2D-EPM) is developed using the variational asymptotic method (VAM). This model significantly reduces the complexity of three-dimensional elasticity problems while preserving essential microstructural characteristics. A Reissner–Mindlin-type formulation is derived, enabling local field reconstruction for detailed stress and displacement evaluation. Model validation is conducted through experimental testing and three-dimensional finite element simulations. The 2D-EPM demonstrates high accuracy, with static analysis errors in load–displacement response within 10% and a maximum modal frequency error of 10.23% in dynamic analysis. The buckling and bending analyses, with or without initial deformation, show strong agreement with the 3D-FEM results, with deviations in the critical buckling load not exceeding 5.23%. Local field reconstruction achieves stress and displacement prediction errors below 2.7%, confirming the model’s fidelity at both global and local scales. Overall, the VAM-based 2D-EPM provides a robust and computationally efficient framework for the structural analysis and optimization of advanced sandwich panels. Full article

In this study, we formulate and analyze a deterministic mathematical model describing the transmission dynamics of pneumonia. A comprehensive stability analysis is conducted for both the disease-free and endemic equilibrium points. The disease-free equilibrium is locally and globally asymptotically stable when the basic reproduction number R₀ < 1, while the endemic equilibrium is locally and globally asymptotically stable when R₀ > 1. To evaluate effective intervention strategies, an optimal control problem is formulated by introducing time-dependent control variables representing awareness campaigns, screening of carriers, and treatment of infected individuals. Applying Pontryagin’s Maximum Principle, the simulation results confirm the effectiveness of the proposed control strategies in reducing the number of infections and mitigating the overall disease burden. The findings offer valuable insights into the control of pneumonia and highlight the potential impact of strategic public health interventions. Full article

This paper investigates distributed optimization problems for multi-agent systems with parametric uncertainties over unbalanced directed communication networks. To settle this class of optimization problems, a continuous-time algorithm is proposed by integrating adaptive control techniques with an output feedback tracking protocol. By systematically employing Lyapunov stability theory, perturbed system analysis, and input-to-state stability theory, we rigorously establish the asymptotic convergence property of the proposed algorithm. A numerical simulation further demonstrates the effectiveness of the algorithm in computing the global optimal solution. Full article

The increasing demand for high-performance power converters for electric vehicle (EV) applications places a significant emphasis on developing effective and robust control strategies for DC-DC converter operation. This paper deals with the development, simulation, and experimental validation of an adaptive Lyapunov-type Nonlinear Sliding Mode Control (L-SMC) strategy for a DC–DC boost converter, addressing significant uncertainties caused by large variations in system parameters (R and L) and ensuring the tracking of a voltage reference. The proposed control strategy employs the Lyapunov stability theory to build an adaptive law to update the parameters of the sliding surface so the system can achieve global asymptotic stability in the presence of uncertainty in inductance, capacitance, load resistance, and input voltage. The nonlinear sliding manifold is also considered, which contributes to a more robust and faster convergence in the controller. In addition, a logic optimization technique was implemented that minimizes switching (chattering) operations significantly, and as a result of this, increases ease of implementation. The proposed L-SMC is validated through both simulation and experimental tests under various conditions, including abrupt increases in input voltage and load disturbances. Simulation results demonstrate that, whether under nominal parameters (R = 320 Ω, L = 2.7 mH) or with parameter variations, the voltage overshoot in all cases remains below 0.5%, while the steady-state error stays under 0.4 V except during the startup, which is a transitional phase lasting a very short time. The current responds smoothly to voltage reference and parameter variations, with very insignificant chattering and overshoot. The current remains stable and constant, with a noticeable presence of a peak with each change in the reference voltage, accompanied by relatively small chattering. The simulation and experimental results demonstrate that adaptive L-SMC achieves accurate voltage regulation, a rapid transient response, and reduces chattering, and the simulation and experimental testing show that the proposed controller has a significantly lower steady-state error, which ensures precise and stable voltage regulation with time. Additionally, the system converges faster for the proposed controller at conversion and is stabilized quickly to the adaptation reference state after the drastic and dynamic change in either the input voltage or load, thus minimizing the settling time. The proposed control approach also contributes to saving energy for the application at hand, all in consideration of minimizing losses. Full article