一类平面自治非线性时滞控制系统的多稳态和混沌

众所周知，平面自治系统即使具有光滑非线性存在，系统也不会出现复杂的动力学行为。本文研究这样的系统存在时滞时，时滞量对系统的动力学行为的影响。通过对一个平面自治非线性系统引入时滞反馈，得到数学模型。利用泛函分析和平均法建立系统平衡态随时滞量变化的失稳机理，研究表明：时滞量平面自治系统动力学行为的影响是本质的．时滞量不但可以使系统出现Hopf分岔，产生周期振动。而且还可以使系统出现多稳态的周期运动或周期吸引子，这些共存的吸引子相碰是导致系统复杂的动力学行为，包括概周期和混沌运动。

Multiple State-Steady Motion and Chaos in a Class of Planar Autonomus Nonlinear System with Delayed Control

It is well known that no complex dynamical behaviors occur in planar autonomous system even with smooth nonlinearities. The effect of time delay on dynamical behaviors was investigated when it exists in such system. The mathematical model was obtained by introducing delayed feedback in a planar autonomous nonlinear system. The functional analysis and averaging method were employed to propose mechanism of stability losing with time delay varying. The obtained results show that the effect of the time delay as control or bifurcation parameter on dynamics is intrinsic. Namely, the time delay may reduce not only Hopf bifurcation and then periodic oscillations, but also occur multistable periodic motions or multistable periodic attractors in the system. They collide to be complex dynamics, such as quasi-periodic motions and chaos.