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On a family of maps with multiple chaotic attractors

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  • Richter, Hendrik

Abstract

Multistability is characterized by the occurrence of multiple coexisting attractors. We introduce a family of maps that possess this property and in particular exhibits coexisting chaotic attractors. In this family not only the maps’ parameters can be varied but also their dimension. So, four types of multistable attractors, equilibria, periodic orbits, quasi-periodic orbits and chaotic attractors can be found for a given dimension.

Suggested Citation

  • Richter, Hendrik, 2008. "On a family of maps with multiple chaotic attractors," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 559-571.
    • Handle: RePEc:eee:chsofr:v:36:y:2008:i:3:p:559-571
    DOI: 10.1016/j.chaos.2007.07.089
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    1. de Souza, Silvio L.T. & Batista, Antonio M. & Caldas, Iberê L. & Viana, Ricardo L. & Kapitaniak, Tomasz, 2007. "Noise-induced basin hopping in a vibro-impact system," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 758-767.
    2. Li, Chunguang & Chen, Guanrong, 2005. "Coexisting chaotic attractors in a single neuron model with adapting feedback synapse," Chaos, Solitons & Fractals, Elsevier, vol. 23(5), pages 1599-1604.
    3. Zhang, Lei & Yi, Zhang, 2007. "Dynamical properties of background neural networks with uniform firing rate and background input," Chaos, Solitons & Fractals, Elsevier, vol. 33(3), pages 979-985.
    4. Chian, Abraham C.-L. & Rempel, Erico L. & Rogers, Colin, 2006. "Complex economic dynamics: Chaotic saddle, crisis and intermittency," Chaos, Solitons & Fractals, Elsevier, vol. 29(5), pages 1194-1218.
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    1. Xu, Quan & Lin, Yi & Bao, Bocheng & Chen, Mo, 2016. "Multiple attractors in a non-ideal active voltage-controlled memristor based Chua's circuit," Chaos, Solitons & Fractals, Elsevier, vol. 83(C), pages 186-200.

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