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An integration method for detecting chaotic responses of nonlinear systems subjected to double excitations
Authors:Y Kang  C-P ChaoC-C Chou  M-H ChuL-H Mu
Institution:a Department of Mechanical Engineering, Chung-Yuan Christian University, Taiwan 320, ROC
b Department of Mechanical Engineering, Tung Nan Technology College, Taiwan 222, ROC
Abstract:A methodology designed for identifying chaos of the nonlinear systems subjected to double excitations is proposed. Based on simulations in this study, it is shown by bifurcation diagram that method of Poincaré sections, the conventional chaos-observing method, fails to pinpoint the onset of chaotic motions with the nonlinear systems subjected to double excitations. To remedy this problem, “Ks integration method” is proposed, which integrates the distance between trajectories and origin in phase plane over an excitation period and designates the obtained integration values as Ks's to take the roles of the sampling points derived by Poincaré sections in constructing bifurcation diagram. This “Ks integration method” is shown capable of providing valuable information in bifurcation diagram such that the parameter range leading to chaos can be easily decided and the number of distinguishable time-domain responses can be determined.
Keywords:Ks Integration method  Bifurcation diagram  Poincaré  sections  Chaos
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