Converting a general 3-d autonomous quadratic system to an extended lorenz-type system

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Original languageEnglish
Pages (from-to)475-488
Journal / PublicationDiscrete and Continuous Dynamical Systems - Series B
Issue number2
Publication statusPublished - Sept 2011


A problem of reducing a general three-dimensional (3-D) autonomous quadratic system to a Lorenz-type system is studied. Firstly, under some necessary conditions for preserving the basic qualitative properties of the Lorenz system, the general 3-D autonomous quadratic system is converted to an extended Lorenz-type system (ELTS) which contains a large class of existing chaotic dynamical systems. Secondly, some different canonical forms of the ELTS are obtained with the aid of various nonsingular linear transformations and normalization techniques. Thirdly, the conjugate systems of the ELTS are defined and discussed. Finally, a sufficient condition for the nonexistence of chaos in such ELTS is derived.

Research Area(s)

  • Bifurcation analysis, Lorenz-type system, Three-dimensional autonomous quadratic system