Megastability: Coexistence of a countable infinity of nested attractors in a periodically-forced oscillator with spatially-periodic damping

Julien C. Sprott1, Sajad Jafari2, Abdul Jalil M. Khalaf3, and Tomasz Kapitaniak4,a

1 Department of Physics, University of Wisconsin-Madison, Madison, WI 53706, USA

2 Biomedical Engineering Department, Amirkabir University of Technology, Tehran
15875-4413, Iran

3 Department of Mathematics, Faculty of Computer Science and Mathematics, University
Of Kufa, Najaf, Iraq

4 Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz,
Poland

Received 2 February 2017 / Received in final form 7 March 2017
Published online 21 June 2017

ABSTRACT

In this paper, we describe a periodically-forced oscillator with spatially-periodic damping. This system has an infinite number of coexisting nested attractors, including limit cycles, attracting tori, and strange attractors.We are aware of no similar example in the literature.

Ref: J. C. Sprott, S. Jafari, A. J. M. Khalaf, and T. Kapitaniak, European Physical Journal - Special Topics 226, 1979-1985 (2017)

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