On a generalized Lorenz canonical form of chaotic systems

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Original languageEnglish
Pages (from-to)1789-1812
Journal / PublicationInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Issue number8
Publication statusPublished - Aug 2002


This paper shows that a large class of systems, introduced in [Čelikovský & Vaněček, 1994; Vaněček & Čelikovský, 1996] as the so-called generalized Lorenz system, are state-equivalent to a special canonical form that covers a broader class of chaotic systems. This canonical form, called generalized Lorenz canonical form hereafter, generalizes the one introduced and analyzed in [Čelikovský & Vaněček, 1994; Vaněčk & Čelikovský, 1996], and also covers the so-called Chen system, recently introduced in [Chen & Ueta, 1999; Ueta & Chen, 2000]. Thus, this new generalized Lorenz canonical form contains as special cases the original Lorenz system, the generalized Lorenz system, and the Chen system, so that a comparison of the structures between two essential types of chaotic systems becomes possible. The most important property of the new canonical form is the parametrization that has precisely a single scalar parameter useful for chaos tuning, which has promising potential in future engineering chaos design. Some other closely related topics are also studied and discussed in the paper.

Research Area(s)

  • Canonical form, Chaos, Chen system, Lorenz system