Transition from stable orbit to chaotic dynamics in hybrid systems of Filippov type with digital sampling

We demonstrate on a representative example of a planar hybrid system with digital sampling a sudden transition from a stable limit cycle to the onset of chaotic dynamics. We show that the scaling law in the size of the attractor is proportional to the digital sampling time $\tau$ for sufficiently small values of $\tau.$ Numerical and analytical results are given. The scaling law changes to a nonlinear law for large values of the sampling time $\tau.$ This phenomenon is explained by the change in the boundedness of the attractor.