CiteWeb id: 19810000079

CiteWeb score: 3200

DOI: 10.1088/0305-4470/14/11/006

It is shown that a dynamical system subject to both periodic forcing and random perturbation may show a resonance (peak in the power spectrum) which is absent when either the forcing or the perturbation is absent. The word resonance is usually applied in physics to cases in which a dynamical system, having periodic oscillations at some frequencies wi, when subject to a periodic forcing of frequencies near one of the wi, shows a marked response. The classical example is that of the forced harmonic oscillator. In this Letter we investigate the possibility of resonance in dynamical systems which (in the absence of forcing) nave a continuum power spectrum, or in other words behave stochastically. In this case the dynamical system has motion on all time scales. We will show that for such systems there can also be a cooperative effect between the internal mechanism and the external periodic forcing. We shall call this effect stochastic resonance. We point out that this is a rather new phenomenon for stochastic dynamical systems and it is likely to have interesting applications. To make clear our result we begin with an example in which a complete analytical theory can be developed. We describe the effect of stochastic resonance for the Langevin equation: dx=(x(a-X2))dt+&dW

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