Search Results (897)

In this paper, we propose a diffusion-type predator–prey interaction model with harvest and disease in prey, and conduct stability analysis and pattern formation analysis on the model. For the temporal model, the asymptotic stability of each equilibrium is analyzed using the linear stability method, and the conditions for Hopf bifurcation to occur near the positive equilibrium are investigated. The simulation results indicate that an increase in infection force might disrupt the stability of the model, while an increase in harvesting intensity would make the model stable. For the spatiotemporal model, a priori estimate for the positive steady state is obtained for the non-existence of the non-constant positive solution using maximum principle and Harnack inequality. The Leray–Schauder degree theory is used to study the sufficient conditions for the existence of non-constant positive steady states of the model, and pattern formation are achieved through numerical simulations. This indicates that the movement of prey and predators plays an important role in pattern formation, and different diffusions of these species may play essentially different effects. Full article

This paper focuses on McKean-Vlasov stochastic differential equations under local Lipschitz conditions. We first introduce the stochastic interacting particle system and prove the propagation of chaos. Then we establish a truncated stochastic theta scheme to approximate the interacting particle system and obtain the strong convergence of the continuous-time truncated stochastic theta scheme to the non-interacting particle system. Furthermore, we study the asymptotical mean square stability of the interacting particle system and the truncated stochastic theta method. Finally, we give one numerical example to verify our theoretical results. Full article

The accordion honeycomb has unique deformation characteristics in cellular materials. This study develops a three-dimensional equivalent Cauchy continuum model (3D-ECM) based on the variational asymptotic method (VAM) to efficiently predict the mechanical response of the accordion honeycomb. The accuracy of the 3D-ECM is validated via quasi-static compression experiments on 3D-printed specimens and detailed 3D finite element simulations (3D-FEM), showing a strong correlation between simulation and experimental data. Parametric analyses reveal that the re-entrant angle, ligament-to-strut length ratio, and thickness ratios significantly affect the equivalent elastic moduli, providing insights into geometric optimization strategies for targeted mechanical performance. Comparative experiments among honeycomb structures with positive, negative, and zero Poisson’s ratios show that the accordion honeycomb achieves superior dimensional stability and tunable stiffness but exhibits lower energy-absorption efficiency due to discontinuous buckling and recovery processes. Further comparison among different ZPR honeycombs confirms that the accordion design offers the highest equivalent modulus in the re-entrant direction. The findings underscore the accordion honeycomb’s promise in scenarios demanding structural reliability, tunable stiffness, and moderate energy absorption. Full article

This paper presents the results of real-time experiments conducted to evaluate the performance of a developed adaptive control scheme applied to control the motion of a real closed-kinematic chain mechanism (CKCM) robot manipulator with two degrees of freedom (DOFs). The developed control scheme, referred to as the decentralized adaptive synchronized control scheme (DASCS), was the result of the combination of model reference adaptive control (MRAC) based on the Lyapunov direct method and the synchronization technique. CKCM manipulators were considered in the experimental study due to their advantages over their open-kinematic chain mechanism (OKCM) manipulator counterparts, such as higher stiffness, better stability, and greater payload. The conducted computer simulation study showed that the DASCS was able to asymptotically converge tracking errors to zero, with all the active joints moving synchronously in a prescribed way. One of the important properties of the DASCS is the independence of robot manipulator dynamics, making it computationally efficient and therefore suitable for real-time applications. The present paper reports findings from experiments in which the DASCS was applied to control the above manipulator and carry out various paths. The DASCS’s performance was compared with that of a traditional adaptive control scheme, namely the SMRACS, when both schemes were applied to track the same paths. Full article

This work investigates fractional stochastic Schrödinger evolution equations in a Hilbert space, incorporating complex potential symmetry and Poisson jumps. We establish the existence of mild solutions via stochastic analysis, semigroup theory, and the Mönch fixed-point theorem. Sufficient conditions for exponential stability are derived, ensuring asymptotic decay. We further explore trajectory controllability, identifying conditions for guiding the system along prescribed paths. A numerical example is provided to validate the theoretical results. Full article

This article concerns a Cournot duopoly game with homogeneous expectations. The cost functions of the two players are assumed to be asymmetric to capture possible asymmetries in firms’ technologies or firms’ input costs. Large values of the speed of adjustment of the players destabilize the Nash Equilibrium (N.E.) and cause the appearance of a chaotic trajectory in the Discrete Dynamical System (D.D.S.). The scope of this article is to control the chaotic dynamics that appear outside the stability field, assuming asymmetric cost functions of the two players. Specifically, one player uses linear costs, while the other uses nonlinear costs (quadratic or cubic). The cubic cost functions are widely used in the Economic Dispatch Problem. The delayed feedback control method is applied by introducing a new control parameter at the D.D.S. It is shown that larger values of the control parameter keep the N.E. locally asymptotically stable even for higher values of the speed of adjustment. Full article

This paper proposes a Distributed Adaptive Regularization Algorithm (DARN) for solving composite non-convex and non-smooth optimization problems in multi-agent systems. The algorithm employs a three-phase iterative framework to achieve efficient collaborative optimization: (1) a local regularized optimization step, which utilizes proximal mappings to enforce strong convexity of weakly convex objectives and ensure subproblem well-posedness; (2) a consensus update based on doubly stochastic matrices, guaranteeing asymptotic convergence of agent states to a global consensus point; and (3) an innovative adaptive regularization mechanism that dynamically adjusts regularization strength using local function value variations to balance stability and convergence speed. Theoretical analysis demonstrates that the algorithm maintains strict monotonic descent under non-convex and non-smooth conditions by constructing a mixed time-scale Lyapunov function, achieving a sublinear convergence rate. Notably, we prove that the projection-based update rule for regularization parameters preserves lower-bound constraints, while spectral decay properties of consensus errors and perturbations from local updates are globally governed by the Lyapunov function. Numerical experiments validate the algorithm’s superiority in sparse principal component analysis and robust matrix completion tasks, showing a 6.6% improvement in convergence speed and a 51.7% reduction in consensus error compared to fixed-regularization methods. This work provides theoretical guarantees and an efficient framework for distributed non-convex optimization in heterogeneous networks. Full article

This paper addresses the problem of optimal stabilization for stochastic dynamical systems characterized by Markov switches and concentration points of jumps, which is a scenario not adequately covered by classical stability conditions. Unlike traditional approaches requiring a strictly positive minimal interval between jumps, we allow jump moments to accumulate at a finite point. Utilizing Lyapunov function methods, we derive sufficient conditions for exponential stability in the mean square and asymptotic stability in probability. We provide explicit constructions of Lyapunov functions adapted to scenarios with jump concentration points and develop conditions under which these functions ensure system stability. For linear stochastic differential equations, the stabilization problem is further simplified to solving a system of Riccati-type matrix equations. This work provides essential theoretical foundations and practical methodologies for stabilizing complex stochastic systems that feature concentration points, expanding the applicability of optimal control theory. Full article

Antivirus (patch) is one of the most powerful tools for defending against malware spread. Distributed patching is superior to its centralized counterpart in terms of significantly lower bandwidth requirement. Under the distributed patching mechanism, a novel malware propagation model with double delays and double saturation effects is proposed. The basic properties of the model are discussed. A pair of thresholds, i.e., the first threshold $R_0$ and the second threshold $R_1$, are determined. It is shown that (a) the model admits no malware-endemic equilibrium if $R_0\le 1$, (b) the model admits a unique patch-free malware-endemic equilibrium and admits no patch-endemic malware-endemic equilibrium if $1<R_0\le R_1$, and (c) the model admits a unique patch-free malware-endemic equilibrium and a unique patch-endemic malware-endemic equilibrium if $R_0>R_1$. A criterion for the global asymptotic stability of the malware-free equilibrium is given. A pair of criteria for the local asymptotic stability of the patch-free malware-endemic equilibrium are presented. A pair of criteria for the local asymptotic stability of the patch-endemic malware-endemic equilibrium are derived. Using cybersecurity terms, these theoretical outcomes have the following explanations: (a) In the case where the first threshold can be kept below unity, the malware can be eradicated through distributed patching. (b) In the case where the first threshold can only be kept between unity and the second threshold, the patches may fail completely, and the malware cannot be eradicated through distributed patching. (c) In the case where the first threshold cannot be kept below the second threshold, the patches may work permanently, but the malware cannot be eradicated through distributed patching. The influence of the delays and the saturation effects on malware propagation is examined experimentally. The relevant conclusions reveal the way the delays and saturation effects modulate these outcomes. Full article

Unknown time-varying parameters, along with mismatched and matched disturbances, exist in hydraulic systems, worsening position tracking performance and even destabilizing systems. To address this issue, this article proposes an adaptive full-state prescribed performance position tracking control for hydraulic systems subject both to unknown time-varying parameters and to mismatched and matched disturbances. First, a smooth nonlinear term is skillfully introduced into the controller design so that it can simultaneously cope with both unknown time-varying parameters and disturbances. Next, by integrating the adaptive technique and the prescribed performance function, an adaptive full-state prescribed performance position tracking controller is developed for hydraulic systems in which both the transient and steady performance of all the control errors can be prescribed. A stability analysis then confirms both the prescribed transient performance and the asymptotic steady performance of all the control errors. Finally, the superiority of the proposed controller is also validated by comparison with simulation results. Full article

Consensus protocols for a multi-agent networked system consist of strategies that align the states of all agents that share information according to a given network topology, despite challenges such as communication limitations, time-varying networks, and communication delays. The special orthogonal group $SO\left(n\right)$ plays a key role in applications from rigid body attitude synchronization to machine learning on Lie groups, particularly in fields like physics-informed learning and geometric deep learning. In this paper, N-agent consensus protocols are proposed on the Lie group $SO\left(4\right)$ and the corresponding tangent bundle $TSO\left(4\right)$, in which the state spaces are $SO{\left(4\right)}^N$ and $TSO{\left(4\right)}^N$, respectively. In particular, when using communication topologies such as a ring graph for which the local stability of non-consensus equilibria is retained in the closed loop, a consensus protocol that leverages a reshaping strategy is proposed to destabilize non-consensus equilibria and produce consensus with almost global stability on $SO{\left(4\right)}^N$ or $TSO{\left(4\right)}^N$. Lyapunov-based stability guarantees are obtained, and simulations are conducted to illustrate the advantages of these proposed consensus protocols. Full article

The asymptotic behavior of discrete Riemann–Liouville fractional difference equations is a fundamental problem with important mathematical and physical implications. In this paper, we investigate a particular case of such an equation of the order $0.5$ subject to a given initial condition. We establish the existence of a unique solution expressed via a Mittag-Leffler-type function. The delta-asymptotic behavior of the solution is examined, and its convergence properties are rigorously analyzed. Numerical experiments are conducted to illustrate the qualitative features of the solution. Furthermore, a neural network-based approximation is employed to validate and compare with the analytical results, confirming the accuracy, stability, and sensitivity of the proposed method. Full article

This paper studies the convergence of distances between sequences of points and that of sequences of points in metric spaces. This investigation is focused on the iterative processes built with composed self-mappings of a cyclic contraction, which can involve more than two nonempty closed subsets in a metric space, which are combined with compositions of a strict contraction with itself, which operates in each of the individual subsets, in any order and any number of mutual compositions. It is admitted, in the most general case, the involvement of any number of repeated compositions of both self-maps with themselves. It is basically seen that, if one of the best-proximity points in the cyclic disposal is unique in a boundedly compact subset of the metric space is sufficient to achieve unique asymptotic cycles formed by a best-proximity point per each adjacent subset. The same property is achievable if such a subset is strictly convex and the metric space is a uniformly convex Banach space. Furthermore, all the sequences with arbitrary initial points in the union of all the subsets of the cyclic disposal converge to such a limit cycle. Full article

This paper presents a composite disturbance-tolerant control framework for quadrotor unmanned aerial vehicles (UAVs). By constructing an enhanced dynamic model that incorporates parameter uncertainties, external disturbances, and actuator faults and considering the inherent underactuated and highly coupled characteristics of the UAV, a novel robust adaptive sliding mode controller (RASMC) is designed. The controller adopts a hierarchical adaptive mechanism and utilizes a dual-loop composite adaptive law to achieve the online estimation of system parameters and fault information. Using the Lyapunov method, the asymptotic stability of the closed-loop system is rigorously proven. Simulation results demonstrate that, under the combined effects of external disturbances and actuator faults, the RASMC effectively suppresses position errors (<0.05 m) and attitude errors (<0.02 radians), significantly outperforming traditional ADRC and LQR control methods. Further analysis shows that the proposed adaptive law enables the precise online estimation of aerodynamic coefficients and disturbance boundaries during actual flights, with estimation errors controlled within ±10%. Moreover, compared to ADRC and LQR, RASMC reduces the settling time by more than 50% and the tracking overshoot by over 70% while using the ($tanh(·)$) approximation to eliminate chattering. Prototype experiments validate the fact that the method achieves centimeter-level trajectory tracking under real uncertainties, demonstrating the superior performance and robustness of the control framework in complex flight missions. Full article

This paper addresses the design of nonfragile state estimators for memristor-based fractional-order neural networks that are subject to stochastic cyber-attacks and hybrid time delays. To mitigate the issue of limited bandwidth during signal transmission, quantitative processing is introduced to reduce network burden and prevent signal blocking. In real network environments, the outputs may be compromised by cyber-attacks, which can disrupt data transmission systems. To better reflect the actual conditions of fractional-order neural networks, a Bernoulli variable is utilized to describe the statistical properties. Additionally, novel conditions are presented to ensure the stochastic asymptotic stability of the augmented error system through a new fractional-order free-matrix-based integral inequality. Finally, the effectiveness of the proposed estimation methods is demonstrated through two numerical simulations. Full article