软弹簧系统在周期小扰动下通向浑沌的道路

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名

邮箱

手机号码

标题

留言内容

验证码

Road to Chaos for a Soft Spring System under Weak Periodic Disturbance

摘要: 本文用Mel'nikov-Holmes方法讨论了软弹簧系统在周期小扰动作用下进入浑沌的途径.发现对于这类系统,由于所加扰动的方式不同,系统会以不同次谐分叉序列通向浑沌,且随着外加频率的变化这种序列会以不同的排列方式把系统导入浑沌.

Abstract: The Mel'nikov-Holmes method is used to discuss the road to chaos for an elastic system with soft spring constant and under weak periodic disturbance. It is found that according to how the disturbance is applied, forced vibration or parametric excitation, the response may pass to chaos through different sequences of subharmonic bifurcations, and that the orders in the sequences may be different for different disturbance frequencies.

[1]	Guckenheimer,J.and P.Holmes,Nonlinear oscillations,Dynamical Systems,and Bifurcation of Vector Fields,Springer-Verlag(1983).
[2]	Morozov,A.D.,On the complete qualitative investigation of the equation of duffing,Differentialhiye Uravneniya,12(1976),241-255.
[3]	Hsieh,D.Y.,On Mathieu equation with damping,J.Math.Phys.,21(1980),722-725.
[4]	Gradshteyn,I.S.and I.M.Ryzhik,Table of Integrals,Series,and Products,Academic Press,8.11(1980).

点击查看大图