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Dynamical Analysis of a Modified Lorenz System

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  • Loong Soon Tee
  • Zabidin Salleh

Abstract

This paper presents another new modified Lorenz system which is chaotic in a certain range of parameters. Besides that, this paper also presents explanations to solve the new modified Lorenz system. Furthermore, some of the dynamical properties of the system are shown and stated. Basically, this paper shows the finding that led to the discovery of fixed points for the system, dynamical analysis using complementary-cluster energy-barrier criterion (CCEBC), finding the Jacobian matrix, finding eigenvalues for stability, finding the Lyapunov functions, and finding the Lyapunov exponents to investigate some of the dynamical behaviours of the system. Pictures and diagrams will be shown for the chaotic systems using the aide of MAPLE in 2D and 3D views. Nevertheless, this paper is to introduce the new modified Lorenz system.

Suggested Citation

  • Loong Soon Tee & Zabidin Salleh, 2013. "Dynamical Analysis of a Modified Lorenz System," Journal of Mathematics, Hindawi, vol. 2013, pages 1-8, December.
    • Handle: RePEc:hin:jjmath:820946
    DOI: 10.1155/2013/820946
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    References listed on IDEAS

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    1. Tigan, Gheorghe & Opriş, Dumitru, 2008. "Analysis of a 3D chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1315-1319.
    2. Yan, Zhenya, 2007. "Hopf bifurcation in the Lorenz-type chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 31(5), pages 1135-1142.
    3. Qi, Guoyuan & Chen, Guanrong & Du, Shengzhi & Chen, Zengqiang & Yuan, Zhuzhi, 2005. "Analysis of a new chaotic system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 352(2), pages 295-308.
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