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Chaos behavior in the discrete Fitzhugh nerve system

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Abstract

The discrete Fitzhugh nerve systems obtained by the Euler method is investigated and it is proved that there exist chaotic phenomena in the sense of Marotto’s definition of chaos. And numerical simulations not only show the consistence with the theoretical analysis but also exhibit the complex dynarnical behaviors, including the ten-periodic orbit, a cascade of period-doubling bifurcation, quasiperiodic orbits and the chaotic orbits and intermittent chaos. The computations of Lyapunov exponents confirm the chaos behaviors. Moreover we also find a strange attractor having the self-similar ohit structure as that of Henon attractor.

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Authors and Affiliations

  1. Department of Mathematics, Hunan Normal University, 410081, Changsha, China

    Zhujun Jing & Yu Chang

  2. Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, 100080, Beijing, China

    Zhujun Jing

  3. lnstitute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, 100080, Beijing, China

    Zhiyuan Jia

Authors
  1. Zhujun Jing
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  2. Zhiyuan Jia
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  3. Yu Chang
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Correspondence to Zhujun Jing.

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Jing, Z., Jia, Z. & Chang, Y. Chaos behavior in the discrete Fitzhugh nerve system. Sci. China Ser. A-Math. 44, 1571–1578 (2001). https://doi.org/10.1007/BF02880796

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  • DOI: https://doi.org/10.1007/BF02880796

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