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.
Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.
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 -