Self-induced stochastic resonance in excitable systems

Cyrill B. Muratov, Eric Vanden-Eijnden, Weinan E

Research output: Contribution to journalArticlepeer-review


The effect of small-amplitude noise on excitable systems with strong time-scale separation is analyzed. It is found that vanishingly small random perturbations of the fast excitatory variable may result in the onset of a deterministic limit cycle behavior, absent without noise. The mechanism, termed self-induced stochastic resonance, combines a stochastic resonance-type phenomenon with an intrinsic mechanism of reset, and no periodic drive of the system is required. Self-induced stochastic resonance is different from other types of noise-induced coherent behaviors in that it arises away from bifurcation thresholds, in a parameter regime where the zero-noise (deterministic) dynamics does not display a limit cycle nor even its precursor. The period of the limit cycle created by the noise has a non-trivial dependence on the noise amplitude and the time-scale ratio between fast excitatory variables and slow recovery variables. It is argued that self-induced stochastic resonance may offer one possible scenario of how noise can robustly control the function of biological systems.

Original languageEnglish (US)
Pages (from-to)227-240
Number of pages14
JournalPhysica D: Nonlinear Phenomena
Issue number3-4
StatePublished - Oct 15 2005


  • Coherence
  • Excitable systems
  • Large deviations
  • Noise-controlled
  • Self-induced stochastic resonance

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics


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