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Synchronization of switch dynamical systems. (English) Zbl 1052.34047

The author considers piecewise continuous dynamical systems, so-called switch systems, modelled by the following autonomous initial value problem, that is

x ˙(t)=f(x(t))=g(x(t))+ i=1 n α i sgn(x i(t) e i ,x(0)=x 0 ,tI=[0,),(1)

where α i , f and g are vector-valued functions, and e i denotes the ith canonical unit vector in n . One of the first goal of the author is to present the assumptions which provide, that (1) defines a dynamical systems. The second purpose is to explore the possibility to synchronize two such switch dynamical systems with chaotic motion. To this end the author uses the Filippov regularization.

MSC:
37D45Strange attractors, chaotic dynamics
34C28Complex behavior, chaotic systems (ODE)
34A36Discontinuous equations
34A60Differential inclusions