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

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 [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 problem, 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.