An integration method for detecting chaotic responses of nonlinear systems subjected to double excitations

Y. Kang*, Chang-Po Chao, C. C. Chou, M. H. Chu, L. H. Mu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

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.

Original languageEnglish
Pages (from-to)1073-1077
Number of pages5
JournalInternational Journal of Non-Linear Mechanics
Volume37
Issue number6
DOIs
StatePublished - 1 Sep 2002

Keywords

  • Bifurcation diagram
  • Chaos
  • K Integration method
  • Poincaré sections

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