周期激励Ueda电路系统的双参数特性分析

Double-parameter Characteristics Analysis of Ueda Circuit Systems with Periodic Excitation

数值计算周期激励Ueda电路系统在双参数平面上的最大Lyapunov指数,得到系统在双参数平面上周期运动、拟周期运动和混沌运动的参数区域。结合单参数分岔图和庞加莱截面图讨论多参数耦合对系统运动稳定性的影响以及系统在参数平面上的分岔混沌过程,表明在不同的参数匹配下系统的局部动力学特性非常复杂,参数之间的相互耦合关系对系统分岔与混沌过程的影响非常明显:当外激励幅值小于1.0时,系统在外激励频率小于1.181或大于1.936的区域内均为拟周期运动;当外激励幅值大于1.0时,系统在外激励频率小于0.9和大于2.5的区域内出现混沌运动和周期运动相交替的现象;选取合适的参数,系统由拟周期运动经锁相退化为周期运动,后经倍周期分岔序列进入混沌运动;在给定系统参数下,当外激励频小于0.2时,系统振子发生颤振。

The top Lyapunov exponent of the Ueda circuit system with periodic excitation on the double-parameter plane is calculated,and the parameter regions of periodic motion,quasi-periodic motion and chaotic motion of the system are obtained.With the single-parameter bifurcation diagrams and Poincarésection maps,the influence of multi-parameter coupling on the system motion stability is discussed,and the bifurcation and chaos processes of the system on the doubleparameter plane are also studied.The results show that the system local dynamic characteristics are very complex under different parameters coupling.The influence of the mutual coupling among the parameters on the process of bifurcation and chaos of the system is very obvious.When the external excitation amplitude is less than1.0,the system exhibits quasiperiodic motion in the region where the external excitation frequency is less than1.181or greater than1.936.When the external excitation amplitude is greater than1.0,the system exhibits periodic motion and chaotic motion alternatively in the range of the external excitation frequency below0.9or above2.5.When the system parameters are selected appropriately,the system motion will evolve into periodic motion from the quasi-periodic motion through phase lock,and then get into chaotic motion through multi-periodic bifurcation.Under the given system parameters,the system oscillator shows chatter motion when the external excitation frequency is less than0.2.