  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.
