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Dynamical properties and simulation of a new Lorenz-like chaotic system

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Abstract

This paper formulates a new three-dimensional chaotic system that originates from the Lorenz system, which is different from the known Lorenz system, Rössler system, Chen system, and includes Lü systems as its special case. By using the center manifold theorem, the stability character of its non-hyperbolic equilibria is obtained. The Hopf bifurcation and the degenerate pitchfork bifurcation, the local character of stable manifold and unstable manifold, are also in detail shown when the parameters of this system vary in the space of parameters. Corresponding bifurcation cases are illustrated by numerical simulations, too. The existence or non-existence of homoclinic and heteroclinic orbits of this system is also studied by both rigorous theoretical analysis and numerical simulation.

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Authors and Affiliations

  1. College of Mathematics and Computational Science, Shenzhen University, Shenzhen, Guangdong, 518060, P.R. China

    Xianyi Li & Qianjun Ou

Authors
  1. Xianyi Li
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  2. Qianjun Ou
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Correspondence to Xianyi Li.

Additional information

This work is partly supported by NNSF of China (grant: 10771094), the Foundation for the High-level Talents of Guangdong Province, and the Foundation for the Innovation Group of Shenzhen University (grant: 000133).

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Li, X., Ou, Q. Dynamical properties and simulation of a new Lorenz-like chaotic system. Nonlinear Dyn 65, 255–270 (2011). https://doi.org/10.1007/s11071-010-9887-z

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  • DOI: https://doi.org/10.1007/s11071-010-9887-z

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