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Self-induced stochastic resonance in excitable systems
Authors:Cyrill B Muratov  Eric Vanden-Eijnden  Weinan E
Institution:

aDepartment of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ 07102, USA

bCourant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA

cDepartment of Mathematics and PACM, Princeton University, Princeton, NJ 08544, USA

Abstract: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.
Keywords:Self-induced stochastic resonance  Coherence  Excitable systems  Large deviations  Noise-controlled
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