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

Marius-F. Danca (1, 2)

1 Department of Mathematics and Computer Science
2 Romanian Institute of Science and Technology

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.

Mots clés: Fractional derivative; Discontinuous dynamical system; Filippov regularization; Differential inclusion; Numerical method

Marius-F. Danca. Chaotic behavior of a class of discontinuous dynamical systems of fractional-order. Nonlinear Dynamics, 2009, 60 (4), pp.525-534. ⟨10.1007/s11071-009-9612-y⟩. ⟨hal-00568402⟩