Existence of periodic solutions for a system of delay differential equations

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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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