Lyapunov exponents for discontinuous dynamical systems of Filip-pov type

The area of discontinuous dynamical systems is almost a young research area, and the enthusiasm and necessity for analyzing 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 the sensitive dependence on initial conditions. Also, one of the most e ective ways to diagnosis chaotic systems is de ning Lyapunov exponents of these systems. Also, de ning and calculating Lyapunov exponents for all discontinuous systems are real challenges. This paper is devoted to de ne Lyapunov exponents for discontinuous dynamical systems of Filippov type in order to investigate chaos for these systems.