Probability distribution of the switching intervals in chaotic pulse streams-a comparative study

In a switched dynamic system the continuous phase flow is accompanied by a stream of switching events. If the system exhibits chaotic behavior this event stream can be used for generating a rectangular wave with chaotic switching times. In this paper the probability distribution of the intervals between the switching times is derived. Two systems different in their continuous state model are treated: a switched linear oscillator and a system with piecewise linear trajectories. It turns out that for both systems the embedded discrete return map is the same but the switching intervals have interesting properties. From this return map the invariant density is calculated. Finally, the probability distributions of the switching intervals for both systems are derived and compared.