Spontaneous Formation of Synchronization Clusters in Homogenous Neuronal Ensembles Induced by Noise and Interaction Delays

Abstract

Spontaneous formation of clusters of synchronized spiking in a structureless ensemble of equal stochastically perturbed excitable neurons with delayed coupling is demonstrated for the first time. The effect is a consequence of a subtle interplay between interaction delays, noise and the excitable character of a single neuron. Dependence of the cluster properties on the time-lag, noise intensity and the synaptic strength is investigated.Collective behavior in large ensembles of physiological and inorganic systems can be reduced to that of coupled oscillators engaged in various synchronization phenomena. In terms of macroscopic coherent rhythms, it may either be the case where all the units are recruited into a giant component or the case of cluster states characterized by exact or in-phase intra-subset and lag inter-subset synchronization. The spontaneous onset of cluster states is of particular interest to neuroscience [1] for the conjectured role in information encoding, as well as for participating in motor coordination or accompanying some neurological disorders. The approach to clustering has mostly relied on modeling neurons as autonomous oscillators, treating separately the question of whether the proposed mechanisms may be robust under noise [2] and transmission delays [3]. We explore a new mechanism which rests on the excitable character of neuronal dynamics and mutual adjustment between noise and time delay to yield the self-organization into functional modules within an otherwise unstructured network.For the instantaneous couplings, the research on populations of excitable neurons has covered pattern formation due to local inhomogeneity [4], or has invoked a scenario where noise enacts a control parameter tuning the dynamics of ensemble averages between the three generic global regimes [5]. Distinct from the layout with complex connection topologies, here it is demonstrated how coupling delays do alter the latter landscape in a significant fashion, giving rise to an effect one may dub the cluster forming time-delay-induced coherence resonance. In part, the strategy to analyze global dynamics rests on deriving the mean-field (MF) approximation for the exact system. The likely gain from the MF treatment is at least twofold: except for allowing one to extrapolate what occurs in the thermodynamic limit N → ∞, it may serve as an auxiliary means to discriminate between the effects of noise and time delay. Unexpectedly, the MF model undergoes a global bifurcation at certain parameter values where the exact system shows an onset of cluster states.Network dynamics and the tools to analyze it -We focus on an N -size population of all-to-all diffusively coupled Fitzhugh-Nagumo neurons, whose local dynamics is set bywhere the activator variables x i embody the membrane potentials, while the recovery variables y i mimic the action of the K + membrane gating channels. c denotes the synaptic strength and τ stands for the coupling delay, both parameters for simplicity assumed homogeneous across the ensemble. The √ 2Dd...

Enhanced corticomuscular coherence by external stochastic noise

“…The phenomenon of enhanced coherence produced by optimal noise has been also described in theoretical models of neurons (Casado, 1997; Neiman et al, 1997; Pikovsky and Kurths, 1997; Lee et al, 1998; Wang et al, 2000; Zhong and Xin, 2000; McMillen and Kopell, 2003; Kreuz et al, 2006; Torcini et al, 2007; Li and Gao, 2008; Guo and Li, 2009; Jiang and Ma, 2009; Franović et al, 2012; Gao and Wang, 2012; Men et al, 2012) and experimentally in physical systems (Lih et al, 1998; Postnov et al, 1998; Giacomelli et al, 2000; Zhong and Xin, 2000, 2001a,b; Calvo et al, 2001; Zhong et al, 2001; Kortlüke et al, 2002; Li and Li, 2003, 2004a,b,c, 2006a,b; Bahar and Moss, 2004; Wang et al, 2010; Xin and Hou, 2006; Perc, 2007; Ermentrout et al, 2008; Li et al, 2008; Perc et al, 2008; Shi and Lang, 2009; Shi and Luo, 2010). It has been experimentally shown that the SR is related to increased local (within one area) and long-range (between different areas) synchrony.…”

Persistence and failure of mean-field approximations adapted to a class of systems of delay-coupled excitable units

“…Apart from the increase of fluctuation amplitudes, enhancing D may give rise to the transition from the stochastically stable FP to the noise-induced spiking. The latter can appear as nearly periodic or irregular depending on c, τ , and D. It is known that in systems of excitable units subjected to D and τ , the length of interspike intervals (ISIs) is influenced by the competition between two characteristic time scales [6,7]. One is set by the self-oscillation "period" T 0 (D) obtained for τ = 0, whereas the other is adjusted with τ .…”

“…The interplay of noise and delays becomes especially intricate if the units making up the system are not self-oscillating, but excitable [5]. For such a setup, the local and collective dynamics rest on the competition between the delay-driven and the noise-induced oscillation modes [6,7].…”

Mean-field approximation of two coupled populations of excitable units

“…This refers to a sequence of local bifurcations under variation of D, τ in and g in , which can be used to highlight the parameter domains giving rise to oscillatory states or those that lead to the amplitude death [36]. In addition, the MF model of an isolated ensemble has also been found to reflect the global bifurcation imminent to the onset of clustering in the exact system [44]. Before proceeding to the main results, several brief remarks on the applied numerical integration schemes are in order.…”