Nondeterministic basin of attraction

Switching dynamical systems occur frequently in many areas of physics and engineering. In this paper we consider a piecewise linear map, that randomly switches in between more than one different functional forms, in any one of the compartments of the phase space. We establish that for such kind of maps there exists a region in the phase space consisting of a special property that, the dynamics of any orbit starting from any particular point, lying inside this region is not deterministic, as any two orbits may find different destinations despite of starting from the same initial point. In other words, even if two orbits start from the same initial point (belonging to the specified region in the phase space), then also they may not converge or diverge together, i.e., one of them may converge to a stable fixed point whereas the other one may diverge to infinity.