Noise-induced mixed-mode oscillations in a relaxation oscillator near the onset of a limit cycle

Document Type

Article

Publication Date

1-1-2008

Abstract

A detailed asymptotic study of the effect of small Gaussian white noise on a relaxation oscillator undergoing a supercritical Hopf bifurcation is presented. The analysis reveals an intricate stochastic bifurcation leading to several kinds of noise-driven mixed-mode oscillations at different levels of amplitude of the noise. In the limit of strong time-scale separation, five different scaling regimes for the noise amplitude are identified. As the noise amplitude is decreased, the dynamics of the system goes from the limit cycle due to self-induced stochastic resonance to the coherence resonance limit cycle, then to bursting relaxation oscillations, followed by rare clusters of several relaxation cycles (spikes), and finally to small-amplitude oscillations (or stable fixed point) with sporadic single spikes. These scenarios are corroborated by numerical simulations. © 2008 American Institute of Physics.

Identifier

41549101373 (Scopus)

Publication Title

Chaos

External Full Text Location

https://doi.org/10.1063/1.2779852

ISSN

10541500

Issue

1

Volume

18

Grant

DMS02-09959

Fund Ref

National Science Foundation

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