具有时滞的高维周期系统的周期解

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

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。

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)= grad G(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 population model is proved.