非线性单摆系统的Hopf分岔  

Hopf bifurcation in nonlinear forced single pendulum systems

作　　者：游泳[1] 

机构地区：[1]北京理工大学珠海学院,广东珠海519088

出　　处：《振动与冲击》2017年第22期104-110,共7页Journal of Vibration and Shock

摘　　要：以单摆系统为例,将Wiggins提出的Hopf分岔条件进行了具体计算。从理论上获得了单摆系统发生次谐分岔的方式,并用数值模拟方法验证了结果的正确性;将Melnikov方法推广到二频驱动情况,由二频驱动单摆的Hopf分岔条件得出存在奇-奇阶次谐分岔和奇-偶阶次谐分岔。数值模拟结果与理论分析一致,表明Melnikov方法可以处理多频驱动系统的Hopf分岔问题。Based on the necessary and sufficient conditions for existence of Hopf bifurcation,the ways to generate subharmonic bifurcation for a single pendulum system were provided. Furthermore,this paper presented an application of the Melnikov method in a two-frequency-driven single pendulum system. The Hopf bifurcation and its conditions were discussed and its application illustrates that the method can solve many problems of Hopf bifurcation in a multi-frequencydriven single pendulum system.

关 键 词：单摆系统 MELNIKOV函数 HOPF分岔 

分 类 号：O322[理学—一般力学与力学基础] O415.6[理学—力学]