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    Please use this identifier to cite or link to this item: https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/53530


    Title: Existence of periodic solutions for a system of delay differential equations
    Authors: Hsu, Cheng-Hsiung;Yang, Suh-Yuh;Yang, Ting-Hui;Yang, Tzi-Sheng
    Contributors: 淡江大學數學學系
    Keywords: Delay differential equation;Poincaré–Bendixson theorem;Periodic solution;Lyapunov functional;Global exponential stability
    Date: 2009-12
    Issue Date: 2011-05-20 09:42:02 (UTC+8)
    Publisher: Kidlington: Pergamon
    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.
    Relation: Nonlinear Analysis: Theory, Methods & Applications 71(12), pp.6222–6231
    DOI: 10.1016/j.na.2009.06.032
    Appears in Collections:[Graduate Institute & Department of Mathematics] Journal Article

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