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Dynamics of deformed Hénon-like map

Author

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  • Gupta, Divya
  • Chandramouli, V.V.M.S.

Abstract

In this paper, we introduce q-deformation on Hénon-like maps and discuss various dynamical properties of newly deformed system, named as q-Hénon map. We describe a method for the construction of superstable periodic cycles and their accumulation on the parameter space for different deformed parameters. At the accumulation, the q-Hénon map undergoes transition from periodic to chaotic behaviour. For restricted range of q, we achieve chaos prior to the canonical Hénon-like maps. This leads to the paradoxical behaviour. Further, we use the concept of heteroclinic web to discuss the heteroclinic bifurcation and the Cantor attractor of infinitely renormalizable q-Hénon maps. Finally, we show that the basin of attraction of q-Hénon maps do not have an escaping region for a particular set of deformed parameters.

Suggested Citation

  • Gupta, Divya & Chandramouli, V.V.M.S., 2022. "Dynamics of deformed Hénon-like map," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    • Handle: RePEc:eee:chsofr:v:155:y:2022:i:c:s0960077921011140
    DOI: 10.1016/j.chaos.2021.111760
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    References listed on IDEAS

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    1. Gregory P. Harmer & Derek Abbott, 1999. "Losing strategies can win by Parrondo's paradox," Nature, Nature, vol. 402(6764), pages 864-864, December.
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