A METHOD TO CALCULATE PERIOD DOUBLING BIFURCATION

Based on physical meaning of Melnikov function,we establish a method to calculateperiod doubling bifurcation and discuss this kind of bifurcation of soft spring Duffingsystem and find that the result is analogous to subharmonic bifurcation,that is,perioddoubling bifurcation will appear if damping is small and amplitude of excitation is big.Thiscoincides with facts of physics.     

A method to calculate period doubling bifurcation

Based on physical meaning of Melnikov function, we establish a method to calculate period doubling bifurcation and discuss this kind of bifurcation of soft spring Duffing system and find that the result is analogous to subharmonic bifurcation, that is, period doubling bifurcation will appear if damping is small and amplitude of excitation is big. Thi coincides with facts of physics.     

计算倍分叉的一种方法

本文从Melnikov函数的物理意义出发,建立了一种计算倍分叉方法.利用这种方法,具体地讨论了软弹簧Duffing系统的倍分叉现象,发现了与次谐分叉相类似结论——即在阻尼小、外激励幅度大时,会出现倍分叉.这样的结果与物理事实是相吻合的.