Stochastic resonance in a discrete neuron with time delay and two different modulation signals

Stochastic resonance in an excitable neuron based on the Rulkov map with noise, delay feedback, low-frequency signal and high-frequency signal is investigated numerically. The results show that there exist an optimal noise intensity, optimal time delay and optimal amplitude of the high-frequency signal at which the phase synchronisation between the low-frequency input signal and the output signal is the best. The Fourier coefficient is calculated to measure the stochastic resonance. It is found that the existence of a maximum in the , and plots is the identifying characteristic of the stochastic resonance phenomenon.

[1]  Kurths,et al.  Doubly stochastic resonance , 2000, Physical review letters.

[2]  J. M. G. Vilar,et al.  Stochastic Multiresonance , 1997 .

[3]  P. McClintock,et al.  LETTER TO THE EDITOR: Vibrational resonance , 2000 .

[4]  Jiang Wang,et al.  Effects of time delay on the stochastic resonance in small-world neuronal networks. , 2013, Chaos.

[5]  V. Berdichevsky,et al.  Stochastic resonance in linear systems subject to multiplicative and additive noise. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[6]  Frank Moss,et al.  Use of behavioural stochastic resonance by paddle fish for feeding , 1999, Nature.

[7]  U. Seifert Stochastic thermodynamics, fluctuation theorems and molecular machines , 2012, Reports on progress in physics. Physical Society.

[8]  Miguel A. F. Sanjuán,et al.  Vibrational resonance in a time-delayed genetic toggle switch , 2013, Commun. Nonlinear Sci. Numer. Simul..

[9]  Guanrong Chen,et al.  Synchronization transitions on small-world neuronal networks: Effects of information transmission delay and rewiring probability , 2008 .

[10]  Robert C. Hilborn,et al.  Coherence resonance in models of an excitable neuron with noise in both the fast and slow dynamics , 2003, q-bio/0309018.

[11]  Z. Duan,et al.  Synchronization transitions on scale-free neuronal networks due to finite information transmission delays. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  Bin Deng,et al.  Vibrational resonance in feedforward network. , 2011, Chaos.

[13]  Polina S. Landa Regular and Chaotic Oscillations , 2001 .

[14]  D. Hu,et al.  Delay-induced vibrational multiresonance in FitzHugh-Nagumo system , 2012 .

[16]  G. Nicolis,et al.  Stochastic aspects of climatic transitions–Additive fluctuations , 1981 .

[17]  Thomas Erneux,et al.  Slow Passage Through a Hopf Bifurcation: From Oscillatory to Steady State Solutions , 1993, SIAM J. Appl. Math..

[18]  Matjaž Perc,et al.  Thoughts out of noise , 2006 .

[19]  Jürgen Kurths,et al.  Vibrational resonance and vibrational propagation in excitable systems , 2003 .

[20]  Bin Deng,et al.  Vibrational resonance in excitable neuronal systems. , 2011, Chaos.

[21]  Miguel A. F. Sanjuán,et al.  Vibrational resonance in biological nonlinear maps , 2012 .

[22]  Robert C. Hilborn A simple model for stochastic coherence and stochastic resonance , 2004 .

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

[24]  Bin Deng,et al.  Vibrational resonance in neuron populations. , 2010, Chaos.

[25]  Frank Moss,et al.  Noise enhancement of information transfer in crayfish mechanoreceptors by stochastic resonance , 1993, Nature.

[26]  J Kurths,et al.  Vibrational resonance in a noise-induced structure. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  J Kurths,et al.  Experimental evidence, numerics, and theory of vibrational resonance in bistable systems. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[28]  Vibrational resonance in a discrete neuronal model with time delay , 2014 .

[29]  Wulfram Gerstner,et al.  SPIKING NEURON MODELS Single Neurons , Populations , Plasticity , 2002 .

[30]  Ke Wang,et al.  Corrigendum to “Global asymptotic stability of a stochastic Lotka–Volterra model with infinite delays” [Commun Nonlinear Sci Numer Simulat 17 (2012) 3115–3123] , 2012 .

[31]  Zhi-Xi Wu,et al.  Influence of synaptic interaction on firing synchronization and spike death in excitatory neuronal networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  M. Perc Stochastic resonance on excitable small-world networks via a pacemaker. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[33]  A. Sutera,et al.  The mechanism of stochastic resonance , 1981 .

[34]  Matjaz Perc,et al.  Minimal model for spatial coherence resonance. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[35]  Matjaz Perc,et al.  Delay-induced multiple stochastic resonances on scale-free neuronal networks. , 2009, Chaos.

[36]  Matjaz Perc,et al.  Effects of correlated Gaussian noise on the mean firing rate and correlations of an electrically coupled neuronal network. , 2010, Chaos.

[37]  Matjaž Perc,et al.  Spatial coherence resonance in neuronal media with discrete local dynamics , 2007 .

[38]  J P Baltanás,et al.  Effects of additive noise on vibrational resonance in a bistable system. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.