Seminar by Jan O. Haerter (Date moved)

Bistability, noise and Parrondo's Paradox

Bistability is ubiquitous in complex systems. For an infinitely-sized mean field system, bistability can be defined as the existence of two stable fixed points. Noise, taken here as unconditionally random transitions between the states of the system, is also common in reality. Real systems, e.g. in biology or social science, are however rarely infinite, nor are constituents connected sufficiently to make a mean field description appropriate. After discussing the classical (single fixed point) Parrondo paradox, where two unbiased games combine to form a biased one, we consider a simple model for bistable dynamical systems when system size and connectivity are varied. We find that noise can act to induce abrupt and irreversible transitions between extremal meta-stable states, functioning as a switch. We comment on possible applications in epigenetics.