Existence of periodic solutions for a system of delay differential equations

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題名:	Existence of periodic solutions for a system of delay differential equations
作者:	Hsu, C.-H.a , Yang, S.-Y.a , Yang, T.-H.b , Yang, T.-S.c
貢獻者:	Department of Mathematics, Tunghai University
關鍵詞:	Delay differential equation;Global exponential stability;Lyapunov functional;Periodic solution;Poincar?-Bendixson theorem
日期:	2009
上傳時間:	2013-06-11T09:02:55Z (UTC)
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 Poincar?-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. ? 2009 Elsevier Ltd. All rights reserved.
關聯:	Nonlinear Analysis, Theory, Methods and Applications Volume 71, Issue 12, 15 December 2009, Pages 6222-6231
顯示於類別:	[應用數學系所] 會議論文

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