反馈周期力对Duffing振子非周期行为的影响

AFFECTION OF DRIVING FORCES WITH FEEDBACK MECHANISM ON NON-PERIODIC BEHAVIOR OF DUFFING OSCILLATOR

探讨了Duffing振子在双驱动力作用下的非周期行为,其中一个驱动力含有反馈机制.共讨论了3种不同的反馈机制.运用Melnikov方法找到了系统发生非周期行为的必要条件,并发现反馈机制可以“遏止”仅由常振幅周期力所导致的系统的浑沌行为,也能够在单一常振幅周期力不能激发浑沌行为的情况下“激励”出非周期行为.为这种非线性系统解决噪声干扰问题提供一条途径.

Non-periodic behaviors of Duffing oscillator driven by two forces are explored. One of the forces possesses feedback mechanism. Three cases with different feedback mechanisms are investigated. D The necessary conditions of the occurence of non-periodic behavior are found by Melnikov method.It is discovered that the feedback mechanism may hold back or stop the chaotic behavior existing for the system exerted by only one periodic force with constant amplitude. Additionally, such mechanism may also excite chaotic behavior which is absent for the system driven by a single periodic force. The results provided a way for nonlinear systems escaping from noisy interference.