Existence of periodic solutions for a system of delay differential equations |
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Authors: | Cheng-Hsiung Hsu Ting-Hui Yang |
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Affiliation: | a Department of Mathematics, National Central University, Jhongli City 32001, Taiwan b Department of Mathematics, Tamkang University, Tamsui, Taipei County 25137, Taiwan c Department of Mathematics, Tunghai University, Taichung 40704, Taiwan |
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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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Keywords: | 34K13 34K20 92B20 |
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