分段常数型自治泛函微分方程的周期解

The Periodic Solution of the Autonomous Functional Differential Equations with a Piecewise Constant Function

研究了含参数α的分段常数型(1)或(2)的自治泛函微分方程(*)。应用“Poincare映射”和推广的Li-Yorke定理,经过推导得到了泛函方程的周期解、振动性和浑沌现象及其对参数的依赖关系。

We consider the autonomous functional differential equations x(t)=f(x(t-1)) (?) with a piecewise constant function f(x). Making use of“Poincare map”and generalized theoren of Li-Yorke,we study the peiodic solution,oscillation and chaos behaviour of the equation.