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

In switched dynamic system the continuous phase ow 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 system di erent in their continuous state model are treated: a switched linear oscillator and a system with piecewise linear trajectories. It turns out that for both system the embedded discrete return map is the same but the switching intervals has 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.