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Bifurcation analysis of a new Lorenz-like chaotic system

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  • Mello, L.F.
  • Messias, M.
  • Braga, D.C.

Abstract

In this paper we study the local codimension one and two bifurcations which occur in a family of three-dimensional vector fields depending on three parameters. An equivalent family, depending on five parameters, was recently proposed as a new chaotic system with a Lorenz-like butterfly shaped attractor and was studied mainly from a numerical point of view, for particular values of the parameters, for which computational evidences of the chaotic attractor was shown. In order to contribute to the understand of this new system we present an analytical study and the bifurcation diagrams of an equivalent three parameter system, showing the qualitative changes in the dynamics of its solutions, for different values of the parameters.

Suggested Citation

  • Mello, L.F. & Messias, M. & Braga, D.C., 2008. "Bifurcation analysis of a new Lorenz-like chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 1244-1255.
    • Handle: RePEc:eee:chsofr:v:37:y:2008:i:4:p:1244-1255
    DOI: 10.1016/j.chaos.2007.11.008
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    References listed on IDEAS

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    1. Zhou, Xiaobing & Wu, Yue & Li, Yi & Wei, Zhengxi, 2008. "Hopf bifurcation analysis of the Liu system," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1385-1391.
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    Cited by:

    1. Belokolos, E.D. & Kharchenko, V.O. & Kharchenko, D.O., 2009. "Chaos in a generalized Lorenz system," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2595-2605.
    2. Dadras, Sara & Momeni, Hamid Reza & Majd, Vahid Johari, 2009. "Sliding mode control for uncertain new chaotic dynamical system," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1857-1862.

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