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On the occurrence of chaos via different routes to chaos: period doubling and border-collision bifurcations

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Abstract

This paper introduces a new 2D piecewise smooth discrete-time chaotic mapping with rarely observed phenomenon – the occurrence of the same chaotic attractor via different and distinguishable routes to chaos: period doubling and border-collision bifurcations as typical futures. This phenomenon is justified by the location of system equilibria of the proposed mapping, and the possible bifurcation types in smooth dissipative systems.

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Authors and Affiliations

  1. Department of Mathematics, University of Tébéssa, (12000), Tébéssa, Algeria

    Z. Elhadj

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  1. Z. Elhadj
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Correspondence to Z. Elhadj.

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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 61, Optimal Control, 2008.

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Elhadj, Z. On the occurrence of chaos via different routes to chaos: period doubling and border-collision bifurcations. J Math Sci 161, 194–199 (2009). https://doi.org/10.1007/s10958-009-9545-5

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