慢变参数激励Duffing系统中的延迟分岔现象及其诱发的簇发振荡

Bifurcation Delay Behaviors and Bursting Oscillations in a Parametrically Excited Duffing’s System

研究了慢变参数激励下Duffing系统的动力学行为.由于慢变参数激励可以周期性地穿越叉型分岔点,周期性的延迟分岔行为可能会发生.探讨了延迟分岔的动力学特性,尤其是基于此产生的簇发振荡.指出了延迟分岔现象所形成的稳定慢流形之间的滞后环是系统中可以观测到簇发振荡主要原因.此外,还分析了初始时间对延迟行为的延迟时间的影响.研究表明,首次延迟行为依赖于系统的初值.但是,随后发生的延迟现象与系统初值无关.

Dynamical behavior of the Duffing’s system with a slowly varying parametric excitation is investigated in this paper.Periodic delayed pitchfork bifurcation behaviors may take place,since the slow parametric excitation can periodically pass through the pitchfork bifurcation point.The dynamical characteristics of bifurcation delay behaviors,especially the resultant bursting oscillations,are discussed.Bifurcation delay behaviors result in hysteresis loops between the stable slow sub-manifolds,which are responsible for bursting oscillations observed in the parametrically excited Duffing’s system.Furthermore,the effect of initial time on the delay time of each delay behavior is analyzed.The result shows that,given enough time,initial time has no influence on the delay time of the delay behavior,although the delay time of the first delay behavior is decided by initial time.