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Dissipative relativistic standard map: Periodic attractors and basins of attraction

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  • Lan, Boon Leong
  • Yapp, Clarence

Abstract

The dissipative relativistic standard map, introduced by Ciubotariu et al. [Ciubotariu C, Badelita L, Stancu V. Chaos in dissipative relativistic standard maps. Chaos, Solitons & Fractals 2002;13:1253–67.], is further studied numerically for small damping in the resonant case. We find that the attractors are all periodic; their basins of attraction have fractal boundaries and are closely interwoven. The number of attractors increases with decreasing damping. For a very small damping, there are thousands of periodic attractors, comprising mostly of the lowest-period attractors of period one or two; the basin of attraction of these lowest-period attractors is significantly larger compared to the basins of the higher-period attractors.

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  • Lan, Boon Leong & Yapp, Clarence, 2008. "Dissipative relativistic standard map: Periodic attractors and basins of attraction," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1300-1304.
    • Handle: RePEc:eee:chsofr:v:37:y:2008:i:5:p:1300-1304
    DOI: 10.1016/j.chaos.2006.10.066
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    Cited by:

    1. Shang, Huilin & Xu, Jian, 2009. "Delayed feedbacks to control the fractal erosion of safe basins in a parametrically excited system," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1880-1896.

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