Most of dynamical systems theory concerns deterministic autonomous systems. However, there is a rapidly growing interest in dynamical systems whose equations of motion are explicitly time-dependent. A special class of these are random dynamical systems which are systems driven by a signal (noise) that admits a probabilistic characterisation.
In this talk we review some recent developments in the understanding of how qualitative changes in the dynamics of random systems may arise. The corresponding bifurcation theory in the deterministic setting is a celebrated corner stone of dynamical systems theory, but its counterpart in the random setting remains much underdeveloped.
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