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Chaotic behavior of a class of discontinuous dynamical systems of fractional-order

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Abstract

In this paper, the chaos persistence in a class of discontinuous dynamical systems of fractional-order is analyzed. To that end, the initial value problem is first transformed, by using the Filippov regularization (Filippov in Differential Equations with Discontinuous Right-Hand Sides, 1988), into a set-valued problem of fractional-order, then by Cellina’s approximate selection theorem (Aubin and Cellina in Differential Inclusions Set-valued Maps and Viability Theory, 1984; Aubin and Frankowska in Set-valued Analysis, 1990). The problem is approximated into a single-valued fractional-order problem, which is numerically solved by using a numerical scheme proposed by Diethelm et al. (Nonlinear Dyn. 29:3–22, 2002). Two typical examples of systems belonging to this class are analyzed and simulated.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Avram Iancu University, Str. Ilie Macelaru, nr. 1A, 400380, Cluj-Napoca, Romania

    Marius-F. Danca

  2. Romanian Institute of Science and Technology, Str. Ciresilor nr. 29, 400487, Cluj-Napoca, Romania

    Marius-F. Danca

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Danca, MF. Chaotic behavior of a class of discontinuous dynamical systems of fractional-order. Nonlinear Dyn 60, 525–534 (2010). https://doi.org/10.1007/s11071-009-9612-y

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