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A filtered Hénon map

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  • Borges, Vinícius S.
  • Eisencraft, Marcio

Abstract

In this paper, we use Lyapunov exponents to analyze how the dynamical properties of the Hénon map change as a function of the coefficients of a linear filter inserted in its feedback loop. We show that the generated orbits can be chaotic or not, depending on the filter coefficients. The dynamics of the system presents complex behavior, including cascades of bifurcations, coexistence of attractors, crises, and “shrimps”. The obtained results are relevant in the context of bandlimited chaos-based communication systems, that have recently been proposed in the literature.

Suggested Citation

  • Borges, Vinícius S. & Eisencraft, Marcio, 2022. "A filtered Hénon map," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    • Handle: RePEc:eee:chsofr:v:165:y:2022:i:p2:s096007792201044x
    DOI: 10.1016/j.chaos.2022.112865
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    References listed on IDEAS

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    1. dos Santos, Vagner & Szezech Jr., José D. & Baptista, Murilo S. & Batista, Antonio M. & Caldas, Iberê L., 2016. "Unstable dimension variability structure in the parameter space of coupled Hénon maps," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 23-28.
    2. Marcio Eisencraft & Renato D. Fanganiello & Luiz A. Baccala, 2009. "Synchronization of Discrete-Time Chaotic Systems in Bandlimited Channels," Mathematical Problems in Engineering, Hindawi, vol. 2009, pages 1-12, June.
    3. Peng, Yuexi & Sun, Kehui & He, Shaobo, 2020. "A discrete memristor model and its application in Hénon map," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
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    Cited by:

    1. Zhu, Wanting & Sun, Kehui & He, Shaobo & Wang, Huihai & Liu, Wenhao, 2023. "A class of m-dimension grid multi-cavity hyperchaotic maps and its application," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).

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