CHAOTIFYING DISCONTINUOUS DYNAMICAL SYSTEMS VIA TIME-DELAY FEEDBACK ALGORITHM

In this paper the anti-control technique of chaos to systems continuous with respect to the state variable using a time-delay feedback technique introduced by Wang, Chen and Yu, is adapted to a class of dynamical systems discontinuous with respect to the state variable. The considered discontinuous initial value problem is transformed into a differential inclusion using the Filippov regularization. Then, certain results on existence and uniqueness of solutions to differential inclusions are used to define our class of discontinuous dynamical systems. Afterwards, introducing an adequate concept of derivative for the considered discontinuous functions, we show that the algorithm for continuous dynamical systems can be adapted to our class of discontinuous problems. Three examples are given.

SYNCHRONIZATION OF SWITCH DYNAMICAL SYSTEMS

The well known synchronization method of Fujisaka and Yamada is adapted to a particular class of piecewise continuous dynamical systems. We give sufficient conditions for the underlying initial value problems, in order to define dynamical systems. For this purpose the Filippov regularization is used, the discontinuous initial value problem being switched into a differential inclusion. A generalized derivative for the considered class of functions is introduced.