Chaos generation in hyperbolic systems


AKHMET M., FEN M. O.

Discontinuity, Nonlinearity, and Complexity, vol.1, no.4, pp.367-386, 2012 (Peer-Reviewed Journal) identifier

  • Publication Type: Article / Article
  • Volume: 1 Issue: 4
  • Publication Date: 2012
  • Journal Name: Discontinuity, Nonlinearity, and Complexity
  • Journal Indexes: Scopus
  • Page Numbers: pp.367-386
  • Keywords: Chaos control, Chaotic attractor, Devaney chaos, Li-Yorke chaos

Abstract

© 2012 L & H Scientific Publishing, LLC.In the present paper, we consider extension of chaos in hyperbolic systems with arbitrary large dimensions. Our investigations comprise chaos in the sense of both Devaney and Li-Yorke. We provide a mechanism for unidirectionally coupled systems through the insertion of chaos from one system to another, where the latter is initially nonchaotic. In our procedure for the chaos extension, we take advantage of chaotic sets of functions to provide mathematically approved results. The theoretical results are supported through the simulations for the extension of chaos generated by a Duffing's oscillator. A control procedure for the extended chaos is demonstrated numerically in the paper.