Ši'lnikov chaos in the generalized lorenz canonical form of dynamical systems

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Detail(s)

Original languageEnglish
Pages (from-to)319-334
Journal / PublicationNonlinear Dynamics
Volume39
Issue number4
Publication statusPublished - Mar 2005

Abstract

This paper studies the generalized Lorenz canonical form of dynamical systems introduced by Čelikovský and Chen [International Journal of Bifurcation and Chaos 12(8) 2002 1789]. It proves the existence of a heteroclinic orbit of the canonical form and the convergence of the corresponding series expansion. The Ši'lnikov criterion along with some technical conditions guarantee that the canonical form has Smale horseshoes and horseshoe chaos. As a consequence it also proves that both the classical Lorenz system and the Chen system have Ši'lnikov chaos. When the system is changed into another ordinary differential equation through a nonsingular one-parameter linear transformation the exact range of existence of Ši'lnikov chaos with respect to the parameter can be specified. Numerical simulation verifies the theoretical results and analysis. © 2005 Springer Science + Business Media Inc.

Research Area(s)

  • Generalized Lorenz canonical form, Heteroclinic orbit, Ši'lnikov criterion

Citation Format(s)

Ši'lnikov chaos in the generalized lorenz canonical form of dynamical systems. / Zhou, Tianshou; Chen, Guanrong; Čelikovský, Sergej.
In: Nonlinear Dynamics, Vol. 39, No. 4, 03.2005, p. 319-334.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review