具有时滞的高维周期系统的周期解

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On the Existence of Periodic Solutions to Higher Dimensional Periodic System with Delay

1.
Department of Mathematics, Beijing Institute of Business, Beijing 100037, P. R. China;
2.
Department of Applied Mechanics, Beijing Institute of Technology, Beijing 100081, P. R. China

摘要: 本文研究具有时滞的高维周期系统x'(t)=A(t,x(t))x(t)+f(t,x(t-τ))与x'(t)=gradG(x(t))+f(t,x(t-τ))的周期解,利用重合度理论,得到保证其存在周期解的充分条件.作为应用,建立了一类对数种群模型周期正解的存在性.
- 时滞 /
- 周期解 /
- 存在性 /
- 重合度
Abstract: In this paper, higher dimensional periodic systems with delay of the form x'(t)=A(t,x(t))x(t)+f(t,x(t-τ)), x'(t)=gradG(x(t))+f(t,x(t-τ)) are considered. Using the coincidence degree method, some sufficient conditions to guarantee the existence of periodic solution for these systems are obtained. As an application of the results, the existence of a positive periodic solution for a logarithmic populat ion model is proved.
- delay /
- periodic solution /
- existence /
- coincidence degree

[1]	Gaines R E,Mawhin J L.Coincidence degree and nonlinear differential equations[A].Lecture Notes in Math[C],567,Berlin:Springer-Verlag,1977.
[2]	Gopalsamy K.Stability and Oscillations in Delay Differential Equations of Population Dynamics[M].Boston:Kluwer Academic Publisher,1992,