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

Domenii publicaţii > Matematica + Tipuri publicaţii > Articol în revistã ştiinţificã

Autori: Marius-F. Danca

Editorial: Springer, Nonlinear Dynamics, 60, p.525-534, 2010.

Rezumat:

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 [1], into a set-valued problem of fractional-order, then by Cellina’s approximate selection theorem [2,3], the problem is approximated into a single-valued fractional-order roblem, which is numerically solved by using a numerical scheme proposed by Diethelm, Ford and Freed [4]. Two typical examples of systems belonging
to this class are analyzed and simulated.

Cuvinte cheie: Fractional derivative, discontinuous dynamical system, Filippov regularization, differential inclusion, numerical method