Noise-induced cooperative dynamics and its control in coupled neuron models

We consider networks of coupled stochastic oscillators. When coupled we find strong collective oscillations, while each unit remains stochastic. In the limit (N\to \infty) we derive a system of integro-delay equations and show analytically that the collective oscillations persist in a large region in parameter. For a regular topology with \emph{few} connections between the oscillators, islands of coherent oscillations are formed, which merge as the amount of topological disor...

We study the dynamics of two neuronal populations weakly and mutually coupled in a multiplexed ring configuration. We simulate the neuronal activity with the stochastic FitzHugh-Nagumo (FHN) model. The two neuronal populations perceive different levels of noise: one population exhibits spiking activity induced by supra-threshold noise (layer 1), while the other population is silent in the absence of inter-layer coupling because its own level of noise is sub-threshold (layer 2...

This paper presents an investigation of the dynamics of two coupled non-identical FitzHugh-Nagumo neurons with delayed synaptic connection. We consider coupling strength and time delay as bifurcation parameters, and try to classify all possible dynamics which is fairly rich. The neural system exhibits a unique rest point or three ones for the different values of coupling strength by employing the pitchfork bifurcation of non-trivial rest point. The asymptotic stability and po...

The counter-intuitive phenomenon of coherence resonance describes a non-monotonic behavior of the regularity of noise-induced oscillations in the excitable regime, leading to an optimal response in terms of regularity of the excited oscillations for an intermediate noise intensity. We study this phenomenon in populations of FitzHugh-Nagumo (FHN) neurons with different coupling architectures. For networks of FHN systems in excitable regime, coherence resonance has been previou...

Time--delayed feedback is exploited for controlling noise--induced motion in coherence resonance oscillators. Namely, under the proper choice of time delay, one can either increase or decrease the regularity of motion. It is shown that in an excitable system, delayed feedback can stabilize the frequency of oscillations against variation of noise strength. Also, for fixed noise intensity, the phenomenon of entrainment of the basic oscillation period by the delayed feedback occ...

Many real-world examples of distributed oscillators involve not only time delays but also attractive (positive) and repulsive (negative) influences in their network interactions. Here, considering such examples, we generalize the Kuramoto model of globally coupled oscillators with time-delayed positive and negative couplings to explore the effects of such couplings in collective phase synchronization. We analytically derive the exact solutions for stable incoherent and cohere...

Oscillators coupled in a network can synchronize with each other to yield a coherent population rhythm. If multiple such networks are coupled together, the question arises whether these rhythms will synchronize. We investigate the impact of noise on this synchronization for strong inhibitory pulse-coupling and find that increasing the noise can synchronize the population rhythms, even if the noisy inputs to different oscillators are completely uncorrelated. Reducing the syste...

We propose a theoretical framework to study the cooperative behavior of dynamically coupled oscillators (DCOs) that possess dynamical interactions. Then, to understand synchronization phenomena in networks of interneurons which possess inhibitory interactions, we propose a DCO model with dynamics of interactions that tend to cause 180-degree phase lags. Employing an approach developed here, we demonstrate that although our model displays synchronization at high frequencies, i...

Despite intensive research, the mechanisms underlying how neurons encode external inputs remain poorly understood. Recent work has focused on the response of a single neuron to a weak, subthreshold periodic signal. By simulating the FitzHugh-Nagumo stochastic model and then using a symbolic method to analyze the firing activity of the neuron, preferred and infrequent spike patterns (defined by the relative timing of the spikes) were detected, whose probabilities encode inform...

The FitzHugh-Nagumo (FHN) model serves as a fundamental neuronal model which is extensively studied across various dynamical scenarios, we explore the dynamics of a scalar FHN oscillator under the influence of white noise. Unlike previous studies, in which extreme events (EE) were observed solely in coupled FHN oscillators, we demonstrate that a single system can exhibit EE induced by noise. Perturbation of the deterministic model in its steady state by random fluctuations re...