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首页> 外文期刊>Nonlinear analysis. Real world applications >Existence and global exponential stability of periodic solution for Cohen-Grossberg neural networks with delays
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Existence and global exponential stability of periodic solution for Cohen-Grossberg neural networks with delays

机译：具时滞的Cohen-Grossberg神经网络周期解的存在性和全局指数稳定性

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摘要

This paper is concerned with the existence and global exponential stability of periodic solutions for a nonlinear periodic system, arising from the description of the states of neurons in delayed Cohen-Grossberg type. By the continuation theorem of coincidence degree theory and Lyapunov functionals technique, we deduce some sufficient conditions ensuring existence as well as global exponential stability of periodic solution. Some existing results are improved and extended. Even corresponding to an autonomous system, our results that these conditions are milder and less restrictive than previous known criteria since the hypothesis of boundedness and differentiability on the activation function are dropped. The theoretical analyses are verified by numerical simulations. (c) 2005 Elsevier Ltd. All rights reserved.
机译：本文关注的是非线性周期系统周期解的存在性和全局指数稳定性，这是由对延迟Cohen-Grossberg型神经元状态的描述引起的。通过重合度理论的连续定理和李雅普诺夫泛函技术，我们推导出了一定的充分条件，确保了周期解的存在性和全局指数稳定性。现有的一些结果得到了改进和扩展。甚至对应于一个自治系统，我们的结果是，这些条件比以前的已知标准更温和，限制更少，因为激活函数的有界性和可微性假设被取消了。通过数值模拟验证了理论分析。 （c）2005 Elsevier Ltd.保留所有权利。

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