非对称型SD振子的混沌阈值  

Chaotic Threshold for the Asymmetrical SD Oscillator

作　　者：陈聚峰[1] 张静[2] 

机构地区：[1]石家庄铁道大学数理系,河北石家庄050043 [2]石家庄邮电职业技术学院基础部,河北石家庄050021

出　　处：《河北师范大学学报（自然科学版）》2015年第1期25-31,共7页Journal of Hebei Normal University：Natural Science

基　　金：国家自然科学基金(11372196);河北省自然科学基金(A2014210104)

摘　　要：基于SD振子,建立了非对称型SD振子模型及其运动方程,其中非对称型振子具有无理恢复力,无法利用常规的非线性方法研究其混沌阈值.为了研究系统的混沌运动,基于分岔的强等价理论,构造了一个与原系统拓扑等价的光滑近似系统,得到了未扰系统同宿轨的解析表达式.在阻尼和外激励的作用下,利用Melnikov方法得到了系统的混沌边界值.最后,利用分岔图和数值模拟研究了近似系统和原系统的混沌运动,验证了理论推导的正确性.Based on SD oscillator,the new model of asymmetrical SD oscillator and its equation of motion are founded.The asymmetrical SD oscillator is a system with an irrational restoring force,which leads to a barrier to detect the chaotic threshold using conventional nonlinear techniques.Based on the theory＇s strongly equivalence for bifurcation,a smooth approximate system,whose behaviors are topologically equivalent to the ones of the original system,is proposed to investigate the chaotic motion.An analytical expression for the unperturbed homoclinic orbits is derived.The Melnikov method is employed to obtain chaotic boundary under the perturbation of damping and external forcing.Finally,bifurcation diagrams and numerical simulations are used to reveal the motion of chaos for the approximate system and the original system,which verify the theoretical derivation.

关 键 词：非对称型SD振子 无理恢复力 拓扑等价 混沌阈值 MELNIKOV方法 

分 类 号：O322[理学—一般力学与力学基础]