Global asymptotic stability for neural network models with distributed delays
Global asymptotic stability for neural network models with distributed delays
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DOI：
10.1016/j.mcm.2009.02.002
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发表时间：
2009-07
期刊：
影响因子：
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通讯作者：
José J. Oliveira
中科院分区：
文献类型：
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作者：
José J. Oliveira
本文通过引入非时滞项的优势条件来消除时滞效应，得到了一般n维时滞微分系统零解的全局渐近稳定性.我们考虑几个延迟微分系统的一般设置，这使我们能够研究，作为子类，著名的神经网络模型的Hopfield，Cohn-Grossberg，双向联想记忆，和静态的S型分布延迟。对于这些系统，我们建立了一个唯一的平衡点的存在性和全局渐近稳定的充分条件，而不使用李雅普诺夫泛函技术。我们的结果改进和推广了已有的结果。
In this paper, we obtain the global asymptotic stability of the zero solution of a general n-dimensional delayed differential system, by imposing a condition of dominance of the non-delayed terms which cancels the delayed effect. We consider several delayed differential systems in general settings, which allow us to study, as subclasses, the well-known neural network models of Hopfield, Cohn–Grossberg, bidirectional associative memory, and static with S-type distributed delays. For these systems, we establish sufficient conditions for the existence of a unique equilibrium and its global asymptotic stability, without using the Lyapunov functional technique. Our results improve and generalize some existing ones.