Mittag-Leffler projective synchronization of Caputo fractional-order reaction–diffusion memristive neural networks with multi-type time delays

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-05-16 DOI:10.1016/j.cnsns.2025.108934

Kai Wu , Ming Tang , Han Ren

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引用次数: 0

Abstract

Neural synchronization plays a crucial role in understanding complex brain functions and driving advancements in artificial intelligence. This paper investigates the Mittag-Leffler projective synchronization in Caputo fractional-order memristive neural networks with reaction–diffusion dynamics and multiple time-varying delays. To address parameter mismatches and achieve synchronization, two adaptive controllers are designed: one for networks with bounded activation functions and another for those with unbounded functions. By leveraging fractional calculus, a novel inequality is derived for fractional-order systems with diverse time-varying delays. This inequality, combined with Green’s formula, Fubini’s theorem, and the Lyapunov functional method, leads to the establishment of algebraic conditions required for achieving Mittag-Leffler projective synchronization in these networks. Finally, numerical simulations validate the theoretical findings, demonstrating the efficacy and reliability of the proposed method.

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多时滞Caputo分数阶反应扩散记忆神经网络的Mittag-Leffler投影同步

神经同步在理解复杂的大脑功能和推动人工智能的进步方面起着至关重要的作用。研究了具有反应扩散动力学和多时变时滞的Caputo分数阶记忆神经网络中的Mittag-Leffler投影同步问题。为了解决参数不匹配并实现同步，设计了两个自适应控制器：一个用于有界激活函数的网络，另一个用于无界激活函数的网络。利用分数阶微积分，导出了具有多种时变时滞的分数阶系统的一个新的不等式。该不等式与Green公式、Fubini定理和Lyapunov泛函方法相结合，建立了在这些网络中实现mittagg - leffler投影同步所需的代数条件。最后，通过数值仿真验证了理论结果，验证了所提方法的有效性和可靠性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.