PERIODIC FLOWS IN SWITCHING DYNAMICAL SYSTEMS THROUGH DISCRETE IMPLICIT MAPPINGS

In this paper, we investigate the periodic flow in a switching dynamical system through an implicit mapping method. By the given accuracy and the transport law, discrete implicit mappings at switching points are obtained and the corresponding interpolation points are achieved. Discrete implicit mappings at non-switching points are obtained by the discretization of differential equations of the switching system and the corresponding interpolation points are also determined. Then the periodic flow expressed by interpolation points in one period is determined. A two-order impulsive system with a pulse at a fixed time is presented as an example. The implicit mapping method may provide a plan for the periodic flows in discontinuous dynamical systems.