Chaotic driven maps: Non-stationary hyperbolic attractor and hyperchaos
Department of Mathematics, Volga State University of Water Transport, 5A, Nesterov str., Nizhny Novgorod 603950, Russia
2 Department of Control Theory, Lobachevsky State University of Nizhny Novgorod, 23, Gagarin Ave., Nizhny Novgorod 603950, Russia
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Received in final form: 19 December 2019
Published online: 26 March 2020
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.
© EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature, 2020