Noisy alias random dynamical systems in recent years have attracted the
interest of physicists and mathematicians, for two basic reasons:
Physically, they add a good deal of realism to the theoretical
models of many natural phenomena which were hitherto modeled by
deterministic dynamical systems, since it has been realized that
noise is almost ubiquitous in reality and often significantly
affects the behaviour of complicated systems. Mathematically, random
dynamical systems present an attractive synthesis of the fields of
stochastics and general dynamical systems in which many branches of
mathematical physics and pure mathematics converge and generate new insights.
In both disciplines, it soon became clear that random dynamical systems
possess a number of interesting new properties, most prominently the
phenomena *noise induced stability, on-off
intermittence*, and *stochastic
bifurcations* also called
*noise induced (phase) transitions*.