Eur. Phys. J. Special Topics 229, 1071-1081 (2020)
https://doi.org/10.1140/epjst/e2020-900252-6

Regular Article

Chaotic driven maps: Non-stationary hyperbolic attractor and hyperchaos

¹ 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

^a e-mail: barabash@itmm.unn.ru

Received: 31 October 2019
Received in final form: 19 December 2019
Published online: 26 March 2020

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.