Abstract
The control effect of recycled noise, generated by the superposition of a primary Gaussian noise source and a secondary source with a constant delay, has been studied in an excitable FitzHugh-Nagumo system. We mainly focus on the performance of noise-induced spike and coherence resonance in a parameter region sub-threshold to supercritical Hopf bifurcation. For fixed noise intensity, simulations show that the coherence (quantitatively measured by R, which is defined as the mean value of the spike interval time T normalized to its mean square root) and the emission velocity of the noise-induced spikes exhibit damped oscillations with the variation of delay time, demonstrating a new kind of multi-resonance phenomenon. Furthermore, the optimal delay times for resonance and the fast emission velocity are related to the inherent frequency of the system. It seems that there are some synchronization effects between the dynamic character of the system and the delay time of recycled noise. Our results give clear information about how one can control the coherence and emission velocity of the noise-induced spike in a rather effective way, by deliberately adjusting the delay time and the fraction of the secondary noise.
Similar content being viewed by others
References
Gammaitoni L, Hänggi P, Jung P, Marchesoni F. Stochastic resonance. Rev Mod Phys, 1998, 70: 223–287
Lindner B, Garcia-Ojalvo J, Neiman A, Schimansky-Geier L. Effects of noise in excitable system. Phys Rep, 2004, 392: 321–424
Christini DJ, Stein KM, Markowitz SM, Mittal S, Slotwiner DJ, Scheiner MA, Iwai S, Lerman BB. Nonlinear-dynamical arrhythmia control in humans. Proc Natl Acad Sci USA, 2001, 98: 5827–5832
Sagués F, Sancho JM, García-Ojalvo J. Spatiotemporal order out of noise. Rev Mod Phys, 2007, 79: 829–882
Hu G, Ditzinger T, Ning CZ, Haken H. Stochastic resonance without external periodic force. Phys Rev Lett, 1993, 71: 807–810
Pikovsky AS, Kurths J. Coherence resonance in a noise-driven excitable system. Phys Rev Lett, 1997, 78: 775–778
Pei X, Bachmann K, Moss F. The detection threshold, noise and stochastic resonance in the Fitzhugh-Nagumo neuron model. Phys Lett A, 1995, 206: 61–65
Hou Z, Rao T, Xin H. Effect of internal noise for rate oscillations during CO oxidation on platinum surfaces. J Chem Phys, 2005, 122: 134708
Gong Y, Hou Z, Xin H. Internal noise stochastic resonance in NO reduction by CO on platinum surfaces. J Phys Chem A, 2005, 109: 2741–2745
Li H, Hou Z, Xin H. Internal noise stochastic resonance for intracellular calcium oscillations in a cell system. Phys Rev E, 2005, 71: 061916
Makarov VA, Nekorkin VI, Velarde MG. Spiking behavior in a noise-driven system combining oscillatory and excitatory properties. Phys Rev Lett, 2001, 86: 3431–3434
DeVille RE L, Vanden-Eijnden E, Muratov CB. Two distinct mechanisms of coherence in randomly perturbed dynamical systems. Phys Rev E, 2005, 72: 031105
Tsimring LS, Pikovsky A. Noise-induced dynamics in bistable systems with delay. Phys Rev Lett, 2001, 87: 250602
Goldobin D, Rosenblum M, Pikovsky A. Controlling oscillator coherence by delayed feedback. Phys Rev E, 2003, 67: 061119
Balanov AG, Janson NB, Schöll E. Control of noise-induced oscillations by delayed feedback. Physica D, 2004, 199: 1–12
Janson NB, Balanov AG, Schöll E. Delayed feedback as a means of control of noise-induced motion. Phys Rev Lett, 2004, 93: 010601
Borromeo M, Marchesoni F. Stochastic synchronization via noise recycling. Phys Rev E, 2007, 75: 041106
Borromeo M, Giusepponi S, Marchesoni F. Recycled noise rectification: An automated Maxwell’s daemon. Phys Rev E, 2006, 74: 031121
Goulding D, Melnik S, Curtin D, Piwonski T, Houlihan J, Gleeson JP, Huyet G. Kramers’ law for a bistable system with time-delayed noise. Phys Rev E, 2007, 76: 031128
Cross MC, Hohenberg PC. Pattern formation outside of equilibrium. Rev Mod Phys, 1993, 65: 854–1014
Keener J, Sneyd J, Mathematical Physiology. New York: Springer-Verlag, 1998. 143–147
Alberts B, Bray D, Lewis J, Raff M, Roberts K, Watson JD. Molecular Biology of the Cell. NewYork: Garland Publishing, 1994
Wei QH, Bechinger C, Leiderer P. Single-file diffusion of colloids in one-dimensional channels. Science, 2000, 287: 625–627
Matthias S, Muller F. Asymmetric pores in a silicon membrane acting as massively parallel Brownian ratchets. Nature (London), 2003, 424: 53–57
Lutz C, Kollmann M, Bechinger C. Single-file diffusion of colloids in one-dimensional channels. Phys Rev Lett, 2004, 93: 026001
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ma, J., Gao, Q. Control of stochastic spike motion in an excitable system via recycled noise. Sci. China Chem. 54, 1504–1509 (2011). https://doi.org/10.1007/s11426-011-4303-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11426-011-4303-1