耦合的非线性振动子的周期运动和同宿运动

Periodic and Homoclinic Motions in Coupled, Nonlinear Oscillators

在强迫激励作用下的耦合的非线性振动子的动力学行为是非常复杂的,而理论分析是非线性振动研究的最基本方式 Melnikov方法是研究系统混沌运动的解析方法之一,笔者正是利用Melnikov方法研究了具有Vanderpol阻尼的这类振动子周期运动、同宿运动和混沌运动,得出这类振动系统产生次谐周期轨和Smale马蹄意义下的混沌的条件。

The dynamic motions of periodically forced, coupled oscillators are very complex; theoretical analysis is essential for their study. Melnikov method is one of the analytic methods for chaotic motion study. Melnikov method is applied to these oscillators with Van der pol damp. Homoclinic and periodic motions are studied. The criteria for the system producing subharmonic periodic orbits and Smale's chaos are obtained. At last the numerical simulation is carried out for this system.