TY - JOUR

T1 - Self-induced stochastic resonance in excitable systems

AU - Muratov, Cyrill B.

AU - Vanden-Eijnden, Eric

AU - E, Weinan

N1 - Funding Information:
C.B.M. is partially supported by NSF via grant DMS02-11864. E.V.-E. is partially supported by NSF via grants DMS01-01439, DMS02-09959 and DMS02-39625. W.E. is partially supported by NSF via grant DMS01-30107.

PY - 2005/10/15

Y1 - 2005/10/15

N2 - 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.

AB - 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.

KW - Coherence

KW - Excitable systems

KW - Large deviations

KW - Noise-controlled

KW - Self-induced stochastic resonance

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U2 - 10.1016/j.physd.2005.07.014

DO - 10.1016/j.physd.2005.07.014

M3 - Article

AN - SCOPUS:25144460267

SN - 0167-2789

VL - 210

SP - 227

EP - 240

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

IS - 3-4

ER -