On-Off Intermittency and Riddled Basins of Attraction in a Coupled Map System

J. Laugesen, E. Mosekilde, Yu. L. Maistrenko and V. L. Maistrenko
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J. Laugesen: Department of Physics, Technical University of Denmark, 2800 Lyngby, Denmark
E. Mosekilde: Department of Physics, Technical University of Denmark, 2800 Lyngby, Denmark
Yu. L. Maistrenko: Institute of Mathematics, National Acdemy of Science of Ukraine, Kiev, Ukraine 252601, Ukraine
V. L. Maistrenko: Institute of Mathematics, National Acdemy of Science of Ukraine, Kiev, Ukraine 252601, Ukraine

Advances in Complex Systems (ACS), 1998, vol. 01, issue 02n03, 161-180

Abstract: The paper examines the appearance of on-off intermittency and riddled basins of attraction in a system of two coupled one-dimensional maps, each displaying type-III intermittency. The bifurcation curves for the transverse destablilization of low periodic orbits embeded in the synchronized chaotic state are obtained. Different types of riddling bifurcation are discussed, and we show how the existence of an absorbing area inside the basin of attraction can account for the distinction between local and global riddling as well as for the distinction between hysteric and non-hysteric blowout. We also discuss the role of the so-called mixed absorbing area that exists immediately after a soft riddling bifurcation. Finally, we study the on-off intermittency that is observed after a non-hysteric blowout bifurcaton.

Keywords: On-Off intermittency; coupled maps; riddled basins of attraction (search for similar items in EconPapers)
Date: 1998
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DOI: 10.1142/S0219525998000120

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