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Horseshoe in a class of planar mappings

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  • Yan Huang
  • Xiao-Song Yang

Abstract

Bursting dynamics of mappings is investigated in this paper. We first present stability analysis of the mappings' equilibria with various parameters. Then for three mappings P , P ¯ , and P ^ with different parameters, we study their powers P 4 , P ¯ 6 , and P ^ 4 . We show that the mappings thus obtained are chaotic by giving a rigorous verification of existence of horseshoes in these mappings. Precisely, we prove that the mapping P ¯ 6 is semiconjugate to the 3-shift mapping; the mappings P 4 and P ^ 4 are semiconjugate to the 4-shift mapping.

Suggested Citation

  • Yan Huang & Xiao-Song Yang, 2006. "Horseshoe in a class of planar mappings," Discrete Dynamics in Nature and Society, Hindawi, vol. 2006, pages 1-10, March.
    • Handle: RePEc:hin:jnddns:067908
    DOI: 10.1155/DDNS/2006/67908
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