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Discrete Dynamics in Nature and Society
Volume 2011, Article ID 681565, 30 pages
Research Article

Coexistence of the Bandcount-Adding and Bandcount-Increment Scenarios

IPVS, University of Stuttgart, Universitätstrasse 38, 70569 Stuttgart, Germany

Received 18 May 2010; Revised 8 January 2011; Accepted 9 January 2011

Academic Editor: J. Kurths

Copyright © 2011 Viktor Avrutin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We investigate the structure of the chaotic domain of a specific one-dimensional piecewise linear map with one discontinuity. In this system, the region of ``robust" chaos is embedded between two periodic domains. One of them is organized by the period-adding scenario whereas the other one by the period-increment scenario with coexisting attractors. In the chaotic domain, the influence of both adjacent periodic domains leads to the coexistence of the recently discovered bandcount adding and bandcount-increment scenarios. In this work, we focus on the explanation of the overall structure of the chaotic domain and a description of the bandcount adding and bandcount increment scenarios.