计算倍分叉的一种方法
A Method to Calculate Period Doubling Bifurcation
-
摘要: 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.Abstract: 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. This coincides with facts of physics.
-
[1] Guckenheimer J.and P.Holmes,Nonlinear Oscillations,Dynamical Systems.and Bifurcations of Vector Fields,Spring-Verlag(1983). [2] 刘曾荣、姚伟国、朱照宣,软弹簧系统在周期小扰动下通向浑沌的道路,应用数学和力学,7,2(1986),103-108. [3] Liu Zheng-rong Some bifurcated and chaotic behavior in soft spring Duffing equation,Proceedings of ICNM,会议文集(1985). [4] Huberman B.A.and J.P.Crutchfield,Chaotic states of anharmonic system in periodic field,Phys.Rev.Lett.,43,23(1979). [5] Chui S.T.and K.B.Ma,Nature of some chaotic states for Duffing's equation,Phys.Rev.A,26,4(1982). [6] 刘曾荣,Melnikov函数的物理意义,科学通报,30-22(1985). -
点击查看大图
计量
- 文章访问数: 1730
- HTML全文浏览量: 91
- PDF下载量: 443
- 被引次数: 0
下载:
