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Chaotic driven maps: Non-stationary hyperbolic attractor and hyperchaos

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Abstract

In this paper we study simple examples of non-autonomous maps having different changing in time chaotic attractors. We present the definition of non-stationary hyperbolic attractor of the driven maps. We rigorously prove the existence of non-stationary hyperbolic attractor in 2D driven map and introduce a hyperchaotic attractor for autonomous 3D map of master-slave structure. Our analysis is based on the auxiliary systems approach and the construction of invariant cones.

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Authors and Affiliations

  1. Department of Mathematics, Volga State University of Water Transport, 5A, Nesterov str., Nizhny Novgorod, 603950, Russia

    Nikita V. Barabash & Vladimir N. Belykh

  2. Department of Control Theory, Lobachevsky State University of Nizhny Novgorod, 23, Gagarin Ave., Nizhny Novgorod, 603950, Russia

    Nikita V. Barabash & Vladimir N. Belykh

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  1. Nikita V. Barabash
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  2. Vladimir N. Belykh
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Correspondence to Nikita V. Barabash.

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Barabash, N.V., Belykh, V.N. Chaotic driven maps: Non-stationary hyperbolic attractor and hyperchaos. Eur. Phys. J. Spec. Top. 229, 1071–1081 (2020). https://doi.org/10.1140/epjst/e2020-900252-6

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  • DOI: https://doi.org/10.1140/epjst/e2020-900252-6

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