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Dynamical Systems pp 37–47Cite as

Complete Bifurcation Behaviors of a Henon Map

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Abstract

In this paper, a methodology to analytically predict the stable and unstable periodic solutions forn-dimensional discrete dynamical systems is applied to investigate the Henon map. The positive and negative iterative mappings of discrete maps are introduced for the mapping structure of the periodic solutions. The complete bifurcation and stability of the stable and unstable periodic solutions with respect to the positive and negative mapping structures is given. The Poincare mapping sections of the Neimark bifurcation of periodic solutions is presented, and the chaotic layers for the discrete system with the Henon map are observed.

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References

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Author information

Authors and Affiliations

  1. Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, Edwardsville, IL, 62026-1805, USA

    Albert C. J. Luo

Authors
  1. Albert C. J. Luo
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  2. Yu Guo
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Corresponding author

Correspondence to Albert C. J. Luo .

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Editors and Affiliations

  1. Edwardsville, Department of Mechanical, Southern Illinois University, Edwardsville, 62026-1805, USA

    Albert C.J. Luo

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Luo, A.C.J., Guo, Y. (2010). Complete Bifurcation Behaviors of a Henon Map. In: Luo, A. (eds) Dynamical Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-5754-2_5

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  • DOI: https://doi.org/10.1007/978-1-4419-5754-2_5

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4419-5753-5

  • Online ISBN: 978-1-4419-5754-2

  • eBook Packages: EngineeringEngineering (R0)

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