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

Cyrill B. Muratov, Eric Vanden Eijnden

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Article number015111
JournalChaos
Volume18
Issue number1
DOIs
StatePublished - 2008

Fingerprint

Relaxation oscillators
relaxation oscillators
Mixed Mode
Limit Cycle
Oscillation
oscillations
cycles
Hopf bifurcation
White noise
Spike
spikes
Stochastic Bifurcation
Coherence Resonance
Relaxation Oscillations
Bursting
Stochastic Resonance
Computer simulation
Gaussian White Noise
white noise
Hopf Bifurcation

ASJC Scopus subject areas

  • Applied Mathematics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Noise-induced mixed-mode oscillations in a relaxation oscillator near the onset of a limit cycle. / Muratov, Cyrill B.; Vanden Eijnden, Eric.

In: Chaos, Vol. 18, No. 1, 015111, 2008.

Research output: Contribution to journalArticle

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