  Grebogi, Ott and Yorke (Phys. Rev. A 38(7), 1988) have investigated the
effect of finite precision on average period length of chaotic maps. They
showed that the average length of periodic orbits ($T$) of a dynamical system
scales as a function of computer precision ($\epsilon$) and the correlation
dimension ($d$) of the chaotic attractor: $T \sim \epsilon^{-d/2}$. In this
work, we are concerned with increasing the average period length which is
desirable for chaotic cryptography applications. Our experiments reveal that
random and chaotic switching of deterministic chaotic dynamical systems yield
higher average length of periodic orbits as compared to simple sequential
switching or absence of switching. To illustrate the application of switching,
a novel generalization of the Logistic map that exhibits Robust Chaos (absence
of attracting periodic orbits) is first introduced. We then propose a
pseudo-random number generator based on chaotic switching between Robust Chaos
maps which is found to successfully pass stringent statistical tests of
randomness.
