摘要
In this paper we mainly study the existence of periodic solutions for a system of delay differential equations representing a simple two-neuron network model of Hopfield type with time-delayed connections between the neurons. We first examine the local stability of the trivial solution, propose some sufficient conditions for the uniqueness of equilibria and then apply the Poincaré-Bendixson theorem for monotone cyclic feedback delayed systems to establish the existence of periodic solutions. In addition, a sufficient condition that ensures the trivial solution to be globally exponentially stable is also given. Numerical examples are provided to support the theoretical analysis.
原文 | ???core.languages.en_GB??? |
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頁(從 - 到) | 6222-6231 |
頁數 | 10 |
期刊 | Nonlinear Analysis, Theory, Methods and Applications |
卷 | 71 |
發行號 | 12 |
DOIs | |
出版狀態 | 已出版 - 15 12月 2009 |