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Si’lnikov homoclinic orbits in a new chaotic system

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  • Jiang, Yongxin
  • Sun, Jianhua

Abstract

In the present paper, a new chaotic system is considered, which is a three-dimensional quadratic system and exhibits two 1-scroll chaotic attractors simultaneously with only three equilibria for some parameters. The existence of Si’lnikov homoclinic orbits in this system has been proven by using the undetermined coefficient method. As a result, the Si’lnikov criterion guarantees that the system has Smale horseshoes. Moreover, the geometric structures of attractors are determined by these homoclinic orbits.

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  • Jiang, Yongxin & Sun, Jianhua, 2007. "Si’lnikov homoclinic orbits in a new chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 150-159.
    • Handle: RePEc:eee:chsofr:v:32:y:2007:i:1:p:150-159
    DOI: 10.1016/j.chaos.2005.10.088
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    References listed on IDEAS

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    1. Čelikovský, Sergej & Chen, Guanrong, 2005. "On the generalized Lorenz canonical form," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1271-1276.
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    Cited by:

    1. Wang, Junwei & Zhao, Meichun & Zhang, Yanbin & Xiong, Xiaohua, 2007. "S˘i’lnikov-type orbits of Lorenz-family systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(2), pages 438-446.

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