The rate matching effect: A hidden property of aperiodic stochastic resonance

We study a system S generating Poisson events, and a corresponding dichotomous signal as well, perturbed by a system P, also generating Poisson events and a corresponding dichotomous signal. The rates of events productions for system and perturbation are g(S) and g(P), respectively. We call S events the events produced by the system S and P events those produced by the perturbation P. We show that this simple model reproduces the essence of recent experimental and theoretical results on aperiodic stochastic resonance. More remarkably, this simplified version of aperiodic stochastic resonance allows us to discover a property that has been overlooked by the earlier research work. The rate matching condition g(S) = g(P) is the border between two distinctly different conditions: For g(S) < g(P), the P events are attractors of the S events and for g(S) > g(P) they become repellers of the S events. The transition from the former to the latter condition is very marked and takes place in a short region of either gS or g(P), depending on which is the parameter changed, thereby resulting in a discontinuous transition. (c) 2007 Elsevier B.V. All rights reserved.