Abstract
Noise-induced complete synchronization and frequency synchronization in coupled spiking and bursting neurons are studied firstly. The effects of noise and coupling are discussed. It is found that bursting neurons are easier to achieve firing synchronization than spiking ones, which means that bursting activities are more important for information transfer in neuronal networks. Secondly, the effects of noise on firing synchronization in a noisy map neuronal network are presented. Noise-induced synchronization and temporal order are investigated by means of the firing rate function and the order index. Firing synchronization and temporal order of excitatory neurons can be greatly enhanced by subthreshold stimuli with resonance frequency. Finally, it is concluded that random perturbations play an important role in firing activities and temporal order in neuronal networks.
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Balenzuela P, Garcĺa-Ojalvo J (2005) On the role of chemical synapse in coupled neurons with noise. Phys Rev E 72:021901
Baltanás JP, Casado JM (2002) Noise-induced resonances in the Hindmarsh–Rose neuronal model. Phys Rev E 65:041915
Barabási AL, Albert R (1999) Emergence of scaling in random networks. Science 286:509–512
Casado JM (2003) Synchronization of two Hodgkin–Huxley neurons due to internal noise. Phys Lett A 310:400–406
Casado JM, Baltanás JP (2003) Phase switching in a system of two noisy Hodgkin–Huxley neurons coupled by a diffusive interaction. Phys Rev E 68:061917
Chua LO, Itoh M, Kocarev L, Eckert K (1993) Chaos synchronization in Chua’s circuits. J Circuits Syst Comput 3:93–108
Eckhorn R, Bauer R (1988) Coherent oscillations: a mechanism of feature linking in the visual cortex. Biol Cybern 60:121–130
Gerstner W, Kistler WM (eds) (2002) Spiking neuron models. Cambridge University Press, Cambridge
Gray CM, Kónig P, Engel AK, Singer W (1989) Oscillatory responses in cat visual cortex exhibit inter-columnar synchronization which reflects global stimulus properties. Nature 338:334–337
He D, Shi P, Stone L (2003) Noise-induced synchronization in realistic models. Phys Rev E 67:027201
Heinzel J, Konig P, Salazar RF (2007) Modulation of synchrony withour changes in firing rates. Cogn Neurodyn 1:225–235
Hindmarsh JL, Rose RM (1984) A model of neuronal bursting using three coupled first order differential equations. Proc R Soc Lond B 221:87–102
Izhikevich EM (2000) Neural excitability, spiking, and bursting. Int J Bifurcat Chaos 10:1171–1266
Jagadeesh B, Gray CM, Ferster D (1992) Visually evoked oscillations of membrane potential in cells of cat visual cortex. Science 257:552–554
Jiang Y (2005) Multiple dynamical resonances in a discrete neuronal model. Phys Rev E 71:057103
Jirsa VK (2008) Dispersion and time delay effects in synchronized spike-burst networks. Cogn Neurodyn 2:29–38
Lee SG, Kim S (1999) Parameter dependence of stochastic resonance in the stochastic Hodgkin–Huxley neuron. Phys Rev E 60:826–830
Li X, Chen G (2003) Synchronization and desynchronization of complex dynamical networks: an engineering viewpoint. IEEE Trans Circuits Syst I 50:1381–1390
Longtin A (1997) Autonomous stochastic resonance in bursting neurons. Phys Rev E 55:868–876
Longtin A, Chialvo DR (1998) Stochastic and deterministic resonances for excitable systems. Phys Rev Lett 81:4012–4015
Miyakawa K, Tanaka T, Isikawa H (2003) Dynamics of a stochastic oscillator in an excitable chemical reaction system. Phys Rev E 67:066206
Neiman A, Sung W (1996) Memory effects on stochastic resonance. Phys Lett A 223:341–347
Neiman A, Silchenko A, Anishchenko V, Schimansky-Geier L (1998) Stochastic resonance: noise-enhanced order. Phys Rev E 58:7118–7125
Pecora LM, Carroll TL (1990) Synchronization in chaotic systems. Phys Rev Lett 64:821–824
Perc M (2005) Spatial coherence resonance in excitable media. Phys Rev E 72:016207
Perc M (2007) Effects of small-world connectivity on noise-induced temporal and spatial order in neural media. Chaos Solitons Fractals 31:280–291
Pikovsky AS, Kurths J (1997) Coherence resonance in a noise-driven excitable system. Phys Rev E 78:775–778
Plesser HE, Geisel T (2001) Signal processing by means of noise. Neurocomputing 38–40:307–312
Postnov DE, Sosnovtseva OV, Han SK, Yim TG (2000) Stochastic synchronization of coupled coherence resonance oscillators. Int J Bifur Chaos 10:2541–2550
Ray R, Sengupta S (2006) Stochastic resonance in underdamped, bistable systems. Phys Lett A 353:364–371
Rosenblum MG, Pikosky AS, Kurths J (1996) Phase synchronization of chaotic oscillators. Phys Rev Lett 76:1804–1807
Rulkov NF, Sushchik MM, Tsimring LS (1995) Generalized synchronization of chaos in directionally coupled chaotic systems. Phys Rev E 51:980–994
Shi X, Lu QS (2005) Firing patterns and complete synchronization of coupled Hindmarsh–Rose neurons. Chin Phys 14:77–85
Shuai JW, Durand DM (1999) Phase synchronization in two coupled chaotic neurons. Phys Lett A 264:289–297
Watts DJ, Strogatz SH (1998) Collective dynamics of “small-world” networks. Nature 393:440–442
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This work was supported by the National Natural Science Foundation of China (Nos.10432010 and 10702023) and Postdoctoral Fund of China (No. 20070410022).
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Shi, X., Wang, Q. & Lu, Q. Firing synchronization and temporal order in noisy neuronal networks. Cogn Neurodyn 2, 195–206 (2008). https://doi.org/10.1007/s11571-008-9055-z
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DOI: https://doi.org/10.1007/s11571-008-9055-z