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Unstable dimension variability structure in the parameter space of coupled Hénon maps

Author

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  • dos Santos, Vagner
  • Szezech Jr., José D.
  • Baptista, Murilo S.
  • Batista, Antonio M.
  • Caldas, Iberê L.

Abstract

Coupled maps have been investigated to model the applications of periodic and chaotic dynamics of spatially extended systems. We have studied the parameter space of coupled Hénon maps and showed that attractors possessing unstable dimension variability (UDV) appear for parameters neighbouring the so called shrimp domains, representing parameters leading to stable periodic behaviour. Therefore, the UDV should be very likely to be found in the same large class of natural and man-made systems that present shrimp domains.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:286:y:2016:i:c:p:23-28
    DOI: 10.1016/j.amc.2016.04.007
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    References listed on IDEAS

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    1. Gallas, Jason A.C., 1994. "Dissecting shrimps: results for some one-dimensional physical models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 202(1), pages 196-223.
    2. Ian Stewart, 2000. "The Lorenz attractor exists," Nature, Nature, vol. 406(6799), pages 948-949, August.
    3. Zhang, Ying-Qian & Wang, Xing-Yuan, 2014. "Spatiotemporal chaos in mixed linear–nonlinear coupled logistic map lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 402(C), pages 104-118.
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    Cited by:

    1. Borges, Vinícius S. & Eisencraft, Marcio, 2022. "A filtered Hénon map," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).

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