Complex dynamics and stability of Hopfield neural networks with delays

S.J. Guo; J.B. Guan; Xinchu Fu

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Complex dynamics and stability of Hopfield neural networks with delays

机译：具有时滞的Hopfield神经网络的复杂动力学和稳定性

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In this paper, by utilising the Lyapunov functional method, we analyse the global asymptotic stability of Hopfield neural networks with delays. We obtain some new sufficient conditions to ensure the global asymptotic stability of the model being independent of delays. By using the Lyapunov second method for special cases, we also get that the equilibrium of the system is locally asymptotically stable when the delay is under a critical value; and when the delay is equal to this value, Hopf bifurcation will occur and the equilibrium is unstable; and when the delay is above the critical value, the system will demonstrate complex dynamics. Finally, numerical simulations are presented to verify the analytical results.

机译：本文利用Lyapunov函数方法，分析了具有时滞的Hopfield神经网络的全局渐近稳定性。我们获得了一些新的充分条件，以确保模型的全局渐近稳定性与延迟无关。通过在特殊情况下使用Lyapunov第二方法，我们还得到了当延迟低于临界值时，系统的平衡是局部渐近稳定的。当延迟等于该值时，将发生Hopf分叉，并且平衡不稳定。当延迟超过临界值时，系统将展示出复杂的动态特性。最后，通过数值模拟验证了分析结果。

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来源
《International journal of systems,control and communications》 |2009年第4期|437-452|共16页
作者
S.J. Guo; J.B. Guan; Xinchu Fu;
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作者单位

Department of Mathematics, Shanghai University, Shanghai 200444, PR China School of Physics and Mathematics, Jiangsu Polytechnic University, Changzhou 213164, PR China;

Department of Mathematics, Shanghai University, Shanghai 200444, PR China;

Department of Mathematics, Shanghai University, Shanghai 200444, PR China;

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正文语种 eng
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关键词
equilibrium; delay; asymptotical stability; hopf bifurcation;

机译：平衡;延迟;无症状的稳定性;Hopf分叉;

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1. Global stability of Hopfield neural networks under dynamical thresholds with distributed delays [J] . Fei-YuZhang, Hai-FengHuo Discrete dynamics in nature and society . 2006,第3期

机译：具有分布时滞的动态阈值下Hopfield神经网络的全局稳定性
2. Global stability of Hopfield neural networks under dynamical thresholds with distributed delays [J] . Fei-Yu Zhang, Hai-Feng Huo Discrete dynamics in nature and society . 2006,第3期

机译：具有分布式延迟的动态阈值下Hopfield神经网络的全局稳定性
3. Global stability of delayed Hopfield neural networks underdynamical thresholds [J] . Fei-YuZhang, Wan-TongLi Discrete dynamics in nature and society . 2005,第1期

机译：动态阈值下的时滞Hopfield神经网络的全局稳定性
4. Global Exponential Stability of the Periodic Solution of a Discrete-Time Complex-Valued Hopfield Neural Network with Delays and Impulses [C] . Valery Covachev, Zlatinka Covacheva International Conference on Advanced Communications and Computation . 2018

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5. Stability analysis of two classes of dynamical systems: General hybrid systems and neural networks with delays [D] . Ye, Hui 1996

机译：两类动力系统的稳定性分析：通用混合动力系统和带时滞的神经网络
6. New delay-interval-dependent stability criteria for switched Hopfield neural networks of neutral type with successive time-varying delay components [O] . R. Manivannan, R. Samidurai, Jinde Cao, 2016

机译：具有连续时变时滞分量的中立型切换Hopfield神经网络的新的依赖于时间间隔的稳定性准则
7. GLOBAL STABILITY OF HOPFIELD NEURAL NETWORKS UNDER DYNAMICAL THRESHOLDS WITH DISTRIBUTED DELAYS [O] . Fei-yu Zhang, Hai-feng Huo 2006

机译：具有分布时滞的动态阈值下的Hopfield神经网络的全局稳定性

Complex dynamics and stability of Hopfield neural networks with delays

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