Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
842222 | Nonlinear Analysis: Theory, Methods & Applications | 2009 | 10 Pages |
Abstract
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.
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Authors
Cheng-Hsiung Hsu, Suh-Yuh Yang, Ting-Hui Yang, Tzi-Sheng Yang,