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S˘i’lnikov-type orbits of Lorenz-family systems

Author

Listed:
  • Wang, Junwei
  • Zhao, Meichun
  • Zhang, Yanbin
  • Xiong, Xiaohua

Abstract

This paper studies the Lorenz-family system which is known to establish a topological connection among the Lorenz, Chen and Lu¨ systems in the parametric space. The existence of S˘i’lnikov heterclinic orbits is proved using an undetermined coefficient method. As a consequence, the S˘i’lnikov criterion along with some technical conditions guarantees that the Lorenz-family system has both Smale horseshoes and horseshoe type of chaos. It is this heteroclinic orbit that determines the geometric structure of the corresponding chaotic attractor.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:375:y:2007:i:2:p:438-446
    DOI: 10.1016/j.physa.2006.10.007
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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.
    2. Jiang, Yongxin & Sun, Jianhua, 2007. "Si’lnikov homoclinic orbits in a new chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 150-159.
    3. Ian Stewart, 2000. "The Lorenz attractor exists," Nature, Nature, vol. 406(6799), pages 948-949, August.
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