Experimental confirmation of the scaling theory for noise-induced crises

Abstract

We investigate experimentally the scaling of the average time τ between intermittent, noise-induced bursts for a chaotic mechanical system near a crisis. The system studied is a periodically driven (frequency f) magnetoelastic ribbon. Theory predicts that for deterministic crises where τ scales as τ∼‖f-${\mathit{f}}_{\mathit{c}}$ ${\mathrm{\Vert }}^{\mathrm{-}\gamma }$ (f<${\mathit{f}}_{\mathit{c}}$, f=${\mathit{f}}_{\mathit{c}}$ at crisis), the characteristic time between noise-induced bursts (f≥${\mathit{f}}_{\mathit{c}}$) should scale as τ∼${\mathrm{\sigma }}^{\mathrm{-}\gamma }$g(‖f-${\mathit{f}}_{\mathit{c}}$‖/σ), where σ is the noise strength and γ is the same in both cases. We determine γ for the low-noise (‘‘deterministic’’) system, then add noise and observe that the scaling for τ is as predicted.