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Role of logistic and Ricker’s maps in appearance of chaos in autonomous quadratic dynamical systems

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Abstract

New existence conditions of a chaotic behavior for wide class of \((n+1)\)-dimensional autonomous quadratic dynamical systems are suggested. It is shown that in all such systems the chaotic dynamics is generated by 1D discrete map by some combination of the logistic map \(f(x) = \lambda x(1 - x); \lambda > 0\) and Ricker’s map \(g(x) = x \exp (\mu - x); \mu > 0\).

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Authors and Affiliations

  1. Department of Applied Mathematics, Dnepropetrovsk National University, Gagarin’s avenue, 72, Dnepropetrovsk, 49050, Ukraine

    Vasiliy Ye. Belozyorov & Svetlana A. Volkova

  2. Department of Computing Engineering and Applied Mathematics, Ukrainian State University of Chemical Technology, Gagarin’s avenue, 8, Dnepropetrovsk, 49005, Ukraine

    Vasiliy Ye. Belozyorov & Svetlana A. Volkova

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  1. Vasiliy Ye. Belozyorov
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  2. Svetlana A. Volkova
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Correspondence to Vasiliy Ye. Belozyorov.

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Belozyorov, V.Y., Volkova, S.A. Role of logistic and Ricker’s maps in appearance of chaos in autonomous quadratic dynamical systems. Nonlinear Dyn 83, 719–729 (2016). https://doi.org/10.1007/s11071-015-2360-2

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  • DOI: https://doi.org/10.1007/s11071-015-2360-2

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