Dynamics of oscillators with periodic dichotomous noise

Publication Type:

Journal Article

Authors:

Source:

Journal of Statistical Physics, Kluwer Academic Publishers-Plenum Publishers, Volume 70, Number 1-2, p.61-76 (1993)

URL:

https://www.scopus.com/inward/record.uri?eid=2-s2.0-21144467355&doi=10.1007%2fBF01053954&partnerID=40&md5=2801cf255be0dc9da9d9c1db58280ef2

Abstract:

The dynamics of bistable oscillators driven by periodic dichotomous noise is described. The stochastic differential equation governing the flow implies smooth trajectories between noise switching events. The dynamics of the two-branched map induced by this flow is a Markov process. Harmonic and quartic models of the bistable potential are studied in the overdamped limit. In the linear (harmonic) case the dynamics can be reduced to a stochastic one-dimensional map with two branches. The moments decay exponentially in this case, although the invariant measure may be multifractal. For strong damping, relaxation induces a cascade leading to a Cantor set and anomalous decay of the density in this case is modeled by a Markov chain. For the physically more realistic case of a quartic potential many additional features arise since the contraction factor is distance dependent. By tuning the barrier-height parameter in the quartic potential, noise-induced transition rates with the characteristics of intermittency are found. © 1993 Plenum Publishing Corporation.