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A new chaotic map with three isolated chaotic regions

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Abstract

Intriguing as the discovery of new chaotic maps is, some new maps also bring new nonlinear phenomena of iterative map behavior. In this paper, we present a simple two-dimensional chaotic map which has three totally separated regions. The twin regions, creating strange and interesting attractors, are close to each other and vertically reflected however not identical in shape, while the distant region, generating a Hénon-like attractor, starts with period-doubling until complete chaos. Given the unusual behavior of the map introduced in this paper, we initially presented linear stability and bifurcation analysis per regions, with Lyapunov exponents and largest exponent computation. Besides the standardized calculations, what we focus here is to find out how a simple map can exhibit different chaotic behaviors in different regions.

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Acknowledgments

The work and the contribution were supported by the project “Smart Solutions in Ubiquitous Computing Environments,” Grant Agency of Excellence, University of Hradec Kralove, Faculty of Informatics and Management.

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  1. Faculty of Informatics and Management, Center for Basic and Applied Research, University of Hradec Kralove, Rokitanskeho 62, 50003, Hradec Kralove, Czech Republic

    Orcan Alpar

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  1. Orcan Alpar
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Correspondence to Orcan Alpar.

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Alpar, O. A new chaotic map with three isolated chaotic regions. Nonlinear Dyn 87, 903–912 (2017). https://doi.org/10.1007/s11071-016-3087-4

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