Generalized Lorenz Canonical Form Revisited

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Detail(s)

Original languageEnglish
Article number2150079
Journal / PublicationInternational Journal of Bifurcation and Chaos
Volume31
Issue number5
Publication statusPublished - Apr 2021

Abstract

This paper completes the description of the generalized Lorenz system (GLS) and hyperbolic generalized Lorenz system (HGLS) along with their canonical forms (GLCF, HGLCF), mostly presented earlier, by deriving explicit state transformation formulas to prove the equivalence between GLS and GLCF, as well as between HGLS and HGLCF. Consequently, complete formulations of the generalized Lorenz canonical systems and forms, and their hyperbolic settings, are obtained and presented. Only potentially chaotic systems are classified, which significantly helps clarify the respective canonical forms. To do so, some tools for systems to exclude chaotic behavior are developed, which are interesting in their own right for general dynamical systems theory. The new insight may inspire future investigations of generalized and canonical formulations of some other types of chaotic systems.

Research Area(s)

  • generalized Lorenz canonical form, Generalized Lorenz system, hyperbolic generalized Lorenz canonical form, hyperbolic generalized Lorenz system