An unusual 3D autonomous quadratic chaotic system with two stable node-foci

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

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Original languageEnglish
Pages (from-to)1061-1083
Journal / PublicationInternational Journal of Bifurcation and Chaos
Issue number4
Publication statusPublished - Apr 2010


This paper reports the finding of an unusual three-dimensional autonomous quadratic Lorenz-like chaotic system which, surprisingly, has two stable node-type of foci as its only equilibria. The new system contains the diffusionless Lorenz system and the Burke-Shaw system, and some others, as special cases. The algebraic form of the new chaotic system is similar to the other Lorenz-type systems, but they are topologically nonequivalent. To further analyze the new system, some dynamical behaviors such as Hopf bifurcation and singularly degenerate heteroclinic and homoclinic orbits, are rigorously proved with simulation verification. Moreover, it is proved that the new system with some specified parameter values has ilnikov-type homoclinic and heteroclinic chaos. © 2010 World Scientific Publishing Company.

Research Area(s)

  • bifurcation, Chaotic attractor, heteroclinic orbit, homoclinic orbit, Lorenz system, singularly degenerate heteroclinic cycle