Coherence resonance in models of an excitable neuron with noise in both the fast and slow dynamics

Abstract We demonstrate the existence of noise-induced regularity (coherence resonance) in both a discrete-time model and a continuous-time model of an excitable neuron. In particular, we show that the effects of noise added to the fast and slow dynamics of the models are significantly different. A Fokker–Planck analysis gives a quantitative explanation of the effects.

[1]  S. Massanés,et al.  Nonadiabatic resonances in a noisy Fitzhugh-Nagumo neuron model , 1999 .

[2]  Sheldon M. Ross,et al.  Stochastic Processes , 2018, Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics.

[3]  S. Han,et al.  Experimental observation of coherence resonance in cascaded excitable systems , 1999 .

[4]  P. Jung,et al.  Optimal intracellular calcium signaling. , 2002, Physical review letters.

[5]  C. Morris,et al.  Voltage oscillations in the barnacle giant muscle fiber. , 1981, Biophysical journal.

[6]  K. Aihara,et al.  Array-enhanced coherence resonance and forced dynamics in coupled FitzHugh-Nagumo neurons with noise. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  J. Kurths,et al.  Coherence Resonance in a Noise-Driven Excitable System , 1997 .

[8]  C. Gardiner.  Handbook of Stochastic Methods , 1983 .

[9]  C. Koch,et al.  Methods in Neuronal Modeling: From Ions to Networks , 1998 .

[10]  Nikolai F Rulkov,et al.  Modeling of spiking-bursting neural behavior using two-dimensional map. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  Liu.  Experimental observation of stochastic resonancelike behavior of autonomous motion in weakly ionized rf magnetoplasmas. , 1995, Physical review letters.

[12]  J. Doob.  Stochastic processes , 1953 .

[13]  Peter Dayan,et al.  Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems , 2001 .

[14]  Dmitry E. Postnov,et al.  INTERACTING COHERENCE RESONANCE OSCILLATORS , 1999 .

[15]  D. J. Aidley.  The physiology of excitable cells , 1971 .

[16]  L Schimansky-Geier,et al.  Analytical approach to the stochastic FitzHugh-Nagumo system and coherence resonance. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[17]  Y. Lai,et al.  Coherence resonance in coupled chaotic oscillators. , 2001, Physical review letters.

[18]  Charles E. Brown.  Coefficient of Variation , 1998 .

[19]  Gerda de Vries,et al.  Bursting as an emergent phenomenon in coupled chaotic maps. , 2001 .

[20]  J. M. Sancho,et al.  Coherence and anticoherence resonance tuned by noise. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  Giacomelli,et al.  Experimental evidence of coherence resonance in an optical system , 2000, Physical review letters.

[22]  J Kurths,et al.  Doubly stochastic coherence via noise-induced symmetry in bistable neural models. , 2003, Physical review letters.

[23]  A. Balanov,et al.  Coherence resonance versus synchronization in a periodically forced self-sustained system. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  G V Osipov,et al.  Coherence resonance in excitable and oscillatory systems: the essential role of slow and fast dynamics. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[25]  J. Kurths,et al.  Array-Enhanced Coherence Resonance , 2001 .

[26]  Y. Horikawa.  Coherence resonance with multiple peaks in a coupled FitzHugh-Nagumo model. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  J. Kurths,et al.  Coherence resonance and polymodality in inhibitory coupled excitable oscillators. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[28]  C. R. Mirasso,et al.  Coherence resonance in chaotic systems , 2001 .

[29]  Distribution of interspike times in noise-driven excitable systems , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[30]  P. Jung,et al.  Stochastic properties of Ca(2+) release of inositol 1,4,5-trisphosphate receptor clusters. , 2002, Biophysical journal.

[31]  K W Young,et al.  Calcium puffs are generic InsP(3)-activated elementary calcium signals and are downregulated by prolonged hormonal stimulation to inhibit cellular calcium responses. , 2001, Journal of cell science.

[32]  A. Longtin.  AUTONOMOUS STOCHASTIC RESONANCE IN BURSTING NEURONS , 1997 .

[33]  N. Rulkov.  Regularization of synchronized chaotic bursts. , 2000, Physical review letters.

[34]  J. Kurths,et al.  Array-enhanced coherence resonance: nontrivial effects of heterogeneity and spatial independence of noise. , 2001, Physical review letters.

[35]  Schimansky-Geier,et al.  Coherence and stochastic resonance in a two-state system , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[36]  H. Haken,et al.  Stochastic resonance without external periodic force. , 1993, Physical review letters.

[37]  W. J. Nowack.  Methods in Neuronal Modeling , 1991, Neurology.

[38]  B Krauskopf,et al.  Excitability and coherence resonance in lasers with saturable absorber. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[39]  Ying-Cheng Lai,et al.  Can noise make nonbursting chaotic systems more regular? , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[40]  Alexander B. Neiman,et al.  Noise-Enhanced Phase Synchronization in Excitable Media , 1999 .

[41]  Alexander B. Neiman,et al.  Coherence resonance in a Hodgkin-Huxley neuron , 1998 .

[42]  Y C Lai,et al.  Noise-enhanced temporal regularity in coupled chaotic oscillators. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[43]  V I Nekorkin,et al.  Spiking behavior in a noise-driven system combining oscillatory and excitatory properties. , 2001, Physical review letters.