短记忆广义Caputo变阶分数系统反应-扩散复杂网络中的分布脉冲同步

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-09-19 DOI:10.1016/j.cnsns.2025.109313

Fengyi Liu , Guoxing Han , Fei Wang , Yongqing Yang

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引用次数: 0

摘要

本文主要研究广义Caputo变阶分数反应扩散复杂网络中的分布脉冲同步问题。首先，基于广义Caputo变阶分数阶微积分和分数阶导数的短时记忆原理，建立了一个新的分数阶类halanay不等式。其次，为了实现同步，采用分布式延迟脉冲控制策略，该策略既考虑了脉冲控制过程中不可避免的时间延迟，又考虑了控制网络的耦合行为；通过设计不同的误差向量，利用新导出的类halanay不等式，结合Lyapunov稳定性理论和Wirtinger不等式，得到了所设计控制方案下的平均同步条件和加权平均同步条件。最后通过仿真实例验证了理论结果的正确性和同步策略的有效性。

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Distributed impulsive synchronization in reaction-diffusion complex networks of generalized Caputo variable-order fractional systems with short memory

This article primarily investigates the distributed impulsive synchronization problem in generalized Caputo variable-order fractional reaction-diffusion complex networks. Firstly, based on generalized Caputo variable-order fractional calculus and the short memory principles of fractional derivative, a novel fractional-order Halanay-like inequality is established. Secondly, to achieve synchronization, a distributed delayed impulsive control strategy is employed, which considers both the inevitable time delay in the impulsive control process and the coupling behavior of the control network. Furthermore, by designing different error vectors and utilizing the newly derived Halanay-like inequality, along with Lyapunov stability theory and Wirtinger inequality, both mean synchronization and weighted mean synchronization conditions are obtained under the designed control scheme. Finally, a simulation example is provided to verify the correctness of our theoretical results and the effectiveness of the synchronization strategy.

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来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.