广义Cohen-Grossberg神经网络的混沌、稳定和分岔共存

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-06-12 DOI:10.1016/j.cnsns.2025.109025

Lianjie Song , Wei Liang , Yongjun Zhang , Xuanxuan Zhang

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引用次数: 0

摘要

本文主要研究一类广义Cohen-Grossberg神经网络的混沌、稳定性和分岔问题。当网络存在一个或两个延迟时，应用回跳排斥理论证明网络在Li-Yorke意义上是混沌的；当网络不存在任何延迟时，应用耦合扩展理论证明网络在Li-Yorke意义上是混沌的。建立了网络稳定性的两个判据。此外，还讨论了具有一个或两个延迟的网络的Fold分岔和neimmark - sacker分岔。给出了三个例子，并通过它们的混沌行为、最大Lyapunov指数的变化趋势和分岔来说明所得结果。

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Coexistence of chaos, stability and bifurcation in a generalized Cohen–Grossberg neural network

This paper is mainly concerned with chaos, stability and bifurcation of a generalized Cohen–Grossberg neural network with two delays or one delay or without any delays. The network is proved to be chaotic in the sense of Li-Yorke by applying the snap-back repeller theory if it has one or two delays, and it is chaotic in the sense of Li-Yorke by using the coupled-expanding theory if the network has not any delays. Two criteria of stability for the network are established. Moreover, Fold and Neimark–Sacker bifurcations of the network with one or two delays are discussed. Three examples are given and their chaotic behavior, the trend of the largest Lyapunov exponents, and bifurcation are demonstrated to illustrate the obtained results.

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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.