Lyapunov exponents for discontinuous dynamical systems of Filippov type

Abstract

‎The area of discontinuous dynamical systems is almost a young research area, and the enthusiasm and necessity for analysing these systems have been growing‎. ‎On the other hand‎, ‎chaos appears in a rather wide class of discontinuous systems‎. ‎One of the most important properties of chaos is sensitive dependence on initial conditions‎. ‎Also,‎ the most effective way to diagnosis chaotic systems is defining Lyapunov exponents of these systems‎. ‎In addition‎, ‎defining and calculating Lyapunov exponents for all discontinuous systems are real challenges‎. ‎This paper is devoted to define Lyapunov exponents for discontinuous dynamical systems of Filippov type in order to investigate chaos for these systems‎.