  In the theory of random dynamical systems (RDS), individuals with different
initial states follow a same law of motion that is stochastically changing with
time | called extrinsic noise. In the present work, intrin- sic noises for each
individual are considered as a perturbation to an RDS. This gives rise to
random Markov systems (RMS) in which the law of mo- tion is still
stochastically changing with time, but individuals also exhibit statistically
independent variations, with each transition having a small probability not to
follow the law. As a consequence, two individuals in an RMS system go through
stochastically distributed periods of synchro- nization and desynchronization,
driven by extrinsic and intrinsic noises respectively. We show that in-sync
time, e.g., escaping from a random attractor, has a symptotic geometric
distribution.
