Wada basin boundaries in switched systems

The Wada basin boundaries of a switched H,non map have been verified for period-2 switching signals [Zhang in Nonlinear Dyn. 73:2221-2229, 2013]. Based upon the auxiliary dynamical system method, the results are extended to the generally switched systems with time-dependent switching. Under some generic assumptions, some sufficient conditions guaranteeing Wada basin boundaries are presented for the periodic switching signals. The results show that switching signals can give rise to this type of basin structure. It suggests that the unpredictability associated to the Wada property can also occur in the switched system.