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    題名: Existence of periodic solutions for a system of delay differential equations
    作者: Hsu, Cheng-Hsiung;Yang, Suh-Yuh;Yang, Ting-Hui;Yang, Tzi-Sheng
    貢獻者: 淡江大學數學學系
    關鍵詞: Delay differential equation;Poincaré–Bendixson theorem;Periodic solution;Lyapunov functional;Global exponential stability
    日期: 2009-12
    上傳時間: 2011-05-20 09:42:02 (UTC+8)
    出版者: Kidlington: Pergamon
    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.
    關聯: Nonlinear Analysis: Theory, Methods & Applications 71(12), pp.6222–6231
    DOI: 10.1016/j.na.2009.06.032
    顯示於類別:[數學學系暨研究所] 期刊論文

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