Cluster synchronization of spiking induced by noise and interaction delays in homogenous neuronal ensembles.

Properties of spontaneously formed clusters of synchronous dynamics in a structureless network of noisy excitable neurons connected via delayed diffusive couplings are studied in detail. Several tools have been applied to characterize the synchronization clusters and to study their dependence on the neuronal and the synaptic parameters. Qualitative explanation of the cluster formation is discussed. The interplay between the noise, the interaction time-delay and the excitable character of the neuronal dynamics is shown to be necessary and sufficient for the occurrence of the synchronization clusters. We have found the two-cluster partitions where neurons are firmly bound to their subsets, as well as the three-cluster ones, which are dynamical by nature. The former turn out to be stable under small disparity of the intrinsic neuronal parameters and the heterogeneity in the synaptic connectivity patterns.

[1]  E. Fetz,et al.  Oscillatory activity in sensorimotor cortex of awake monkeys: synchronization of local field potentials and relation to behavior. , 1996, Journal of neurophysiology.

[2]  Lijian Yang,et al.  Propagation of firing rate by synchronization and coherence of firing pattern in a feed-forward multilayer neural network. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[4]  L Schimansky-Geier,et al.  Regular patterns in dichotomically driven activator-inhibitor dynamics. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  W Singer,et al.  Visual feature integration and the temporal correlation hypothesis. , 1995, Annual review of neuroscience.

[6]  W. Singer,et al.  Dynamic predictions: Oscillations and synchrony in top–down processing , 2001, Nature Reviews Neuroscience.

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

[8]  Yang Gao,et al.  Oscillation propagation in neural networks with different topologies. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  Jose Luis Perez Velazquez,et al.  Coordinated Activity in the Brain , 2009 .

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

[11]  Igor Franović,et al.  Spontaneous formation of synchronization clusters in homogenous neuronal ensembles induced by noise and interaction delays. , 2012, Physical review letters.

[12]  J. Kaiser,et al.  Human gamma-frequency oscillations associated with attention and memory , 2007, Trends in Neurosciences.

[13]  Antonio Politi,et al.  Irregular collective behavior of heterogeneous neural networks. , 2010, Physical review letters.

[14]  Philipp Hövel,et al.  Time-delayed feedback in neurosystems , 2008, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[15]  Menghui Li,et al.  Spontaneous formation of dynamical groups in an adaptive networked system , 2010, ArXiv.

[16]  Igor Goychuk,et al.  Channel noise and synchronization in excitable membranes , 2003 .

[17]  M. Rosenblum,et al.  Controlling synchronization in an ensemble of globally coupled oscillators. , 2004, Physical review letters.

[18]  Eric Vanden-Eijnden,et al.  Noise-induced mixed-mode oscillations in a relaxation oscillator near the onset of a limit cycle. , 2008, Chaos.

[19]  E Weinan,et al.  Self-induced stochastic resonance in excitable systems , 2005 .

[20]  Jianfeng Feng,et al.  Stability of synchronous oscillations in a system of Hodgkin-Huxley neurons with delayed diffusive and pulsed coupling. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  David Terman,et al.  Mathematical foundations of neuroscience , 2010 .

[22]  J. García-Ojalvo,et al.  Effects of noise in excitable systems , 2004 .

[23]  L. M. Ward,et al.  Synchronous neural oscillations and cognitive processes , 2003, Trends in Cognitive Sciences.

[24]  K. Okuda.  Variety and generality of clustering in globally coupled oscillators , 1993 .

[25]  Simona Olmi,et al.  Collective chaos in pulse-coupled neural networks , 2010, 1010.2957.

[26]  Mark D. McDonnell,et al.  The benefits of noise in neural systems: bridging theory and experiment , 2011, Nature Reviews Neuroscience.

[27]  G. Buzsáki,et al.  Neuronal Oscillations in Cortical Networks , 2004, Science.

[28]  H. Hasegawa.  Stochastic bifurcation in FitzHugh–Nagumo ensembles subjected to additive and/or multiplicative noises , 2006, cond-mat/0610028.

[29]  N. Buric,et al.  Dynamics of FitzHugh-Nagumo excitable systems with delayed coupling. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[30]  E. Manjarrez,et al.  Internal stochastic resonance in the coherence between spinal and cortical neuronal ensembles in the cat , 2002, Neuroscience Letters.

[31]  L. Schimansky-Geier,et al.  Noise-controlled oscillations and their bifurcations in coupled phase oscillators. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  Fatihcan M. Atay,et al.  Complex Time-Delay Systems , 2010 .

[33]  Christian Hauptmann,et al.  Effective desynchronization by nonlinear delayed feedback. , 2005, Physical review letters.

[34]  S. Strogatz,et al.  Time Delay in the Kuramoto Model of Coupled Oscillators , 1998, chao-dyn/9807030.

[35]  D. Valenti,et al.  Dynamics of a FitzHugh-Nagumo system subjected to autocorrelated noise , 2008, 0810.1432.

[36]  M. Rosenblum,et al.  Delayed feedback control of collective synchrony: an approach to suppression of pathological brain rhythms. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[37]  Steven H. Strogatz,et al.  Nonlinear dynamics: Death by delay , 1998, Nature.

[38]  Sen,et al.  Experimental evidence of time-delay-induced death in coupled limit-cycle oscillators , 1998, Physical review letters.

[39]  N. Buric,et al.  Mean field approximation for noisy delay coupled excitable neurons , 2010, 1003.5187.

[40]  Jonathan E. Rubin,et al.  Coherent Behavior in Neuronal Networks , 2009 .

[41]  S Coombes,et al.  Clustering through postinhibitory rebound in synaptically coupled neurons. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[42]  G. Cecchi,et al.  Scale-free brain functional networks. , 2003, Physical review letters.

[43]  O. Sporns,et al.  Complex brain networks: graph theoretical analysis of structural and functional systems , 2009, Nature Reviews Neuroscience.

[44]  A. Oliviero,et al.  Movement-related changes in synchronization in the human basal ganglia. , 2002, Brain : a journal of neurology.

[45]  Viktor K. Jirsa,et al.  Dispersion and time delay effects in synchronized spike–burst networks , 2008, Cognitive Neurodynamics.

[46]  A R Bulsara,et al.  Noisy FitzHugh-Nagumo model: from single elements to globally coupled networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[47]  N. Buric,et al.  Influence of interaction delays on noise-induced coherence in excitable systems. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[48]  Mingzhou Ding,et al.  Enhancement of neural synchrony by time delay. , 2004, Physical review letters.

[49]  Ritwik K Niyogi,et al.  Learning-rate-dependent clustering and self-development in a network of coupled phase oscillators. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[50]  T. Geisel,et al.  Delay-induced multistable synchronization of biological oscillators , 1998 .

[51]  Dirk Roose,et al.  Numerical bifurcation analysis of delay differential equations using DDE-BIFTOOL , 2002, TOMS.

[52]  E. M. Pinches,et al.  The role of synchrony and oscillations in the motor output , 1999, Experimental Brain Research.

[53]  Hildegard Meyer-Ortmanns,et al.  Noise as control parameter in networks of excitable media: Role of the network topology. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[54]  Eric Vanden-Eijnden,et al.  Two distinct mechanisms of coherence in randomly perturbed dynamical systems. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[55]  Nikolai F. Rulkov,et al.  Synchronized Action of Synaptically Coupled Chaotic Model Neurons , 1996, Neural Computation.

[56]  P. Fries.  A mechanism for cognitive dynamics: neuronal communication through neuronal coherence , 2005, Trends in Cognitive Sciences.

[57]  O. Sporns,et al.  Organization, development and function of complex brain networks , 2004, Trends in Cognitive Sciences.

[58]  J. Donoghue,et al.  Oscillations in local field potentials of the primate motor cortex during voluntary movement. , 1993, Proceedings of the National Academy of Sciences of the United States of America.

[59]  Bernardo Spagnolo,et al.  Suppression of noise in FitzHugh-Nagumo model driven by a strong periodic signal [rapid communication] , 2005 .

[60]  Hideo Hasegawa,et al.  Dynamical mean-field theory of spiking neuron ensembles: response to a single spike with independent noises. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[61]  J. Rinzel,et al.  Clustering in globally coupled inhibitory neurons , 1994 .

[62]  J. Martinerie,et al.  The brainweb: Phase synchronization and large-scale integration , 2001, Nature Reviews Neuroscience.

[63]  Igor Franović,et al.  Functional motifs: a novel perspective on burst synchronization and regularization of neurons coupled via delayed inhibitory synapses , 2011 .