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We continue the work of a series of previous studies of a mathematical model that describes the mean-field limit behavior of a homogeneous network of excitatory point spiking neurons. Contrary to other models, here noise is intrinsic to the…
We consider an excitatory random network of leaky integrate-and-fire pulse coupled neurons. The neurons are connected as in a directed Erd\"os-Renyi graph with average connectivity $<k>$ scaling as a power law with the number of neurons in…
Gap-junctional coupling is an important way of communication between neurons and other excitable cells. Strong electrical coupling synchronizes activity across cell ensembles. Surprisingly, in the presence of noise synchronous oscillations…
In this paper, the complete synchronization problem of linearly coupled neural networks with reaction-diffusion terms and time-varying delays via aperiodically intermittent pinning control is investigated. The coupling matrix for the…
The presence of correlated noise, arising from a mixture of independent fluctuations and a common noisy input shared across the neural population, is a ubiquitous feature of neural circuits, yet its impact on collective network dynamics…
Using network models consisting of gap junction coupled Wang-Buszaki neurons, we demonstrate that it is possible to obtain not only synchronous activity between neurons but also a variety of constant phase shifts between 0 and \pi. We call…
For a class of coupled limit cycle oscillators, we give a condition on a linear coupling operator that is necessary and sufficient for exponential stability of the synchronous solution. We show that with certain modifications our method of…
We investigate the performance of sparsely-connected networks of integrate-and-fire neurons for ultra-short term information processing. We exploit the fact that the population activity of networks with balanced excitation and inhibition…
We experimentally demonstrate the occurrence of various synchronized states in coupled piece-wise linear time-delayed electronic circuits using dynamic environment coupling where the environment has its own intrinsic dynamics via feedback…
Intermittent synchronization is observed in a variety of different experimental settings in physics and beyond and is an established research topic in nonlinear dynamics. When coupled oscillators exhibit relatively weak, intermittent…
We extensively explore networks of weakly unbalanced, leaky integrate-and-fire (LIF) neurons for different coupling strength, connectivity, and by varying the degree of refractoriness, as well as the delay in the spike transmission. We find…
Pulse-coupled spiking neural networks are a powerful tool to gain mechanistic insights into how neurons self-organize to produce coherent collective behavior. These networks use simple spiking neuron models, such as the $\theta$-neuron or…
The "edge of chaos" phase transition in artificial neural networks is of renewed interest in light of recent evidence for criticality in brain dynamics. Statistical mechanics traditionally studied this transition with connectivity $k$ as…
Spiking Neural Networks (SNNs) capture the information processing mechanism of the brain by taking advantage of spiking neurons, such as the Leaky Integrate-and-Fire (LIF) model neuron, which incorporates temporal dynamics and transmits…
Using a stochastic generalization of the Hodgkin–Huxley model, we consider the influence of intrinsic channel noise on the synchronization between the spiking activity of the excitable membrane and an externally applied periodic…
We study the deterministic dynamics of networks N composed by m non identical, mutually pulse-coupled cells. We assume weighted, asymmetric and positive (cooperative) interactions among the cells, and arbitrarily large values of m. We…
We present here some studies on noise-induced order and synchronous firing in a system of bidirectionally coupled generic type-I neurons. We find that transitions from unsynchronized to completely synchronized states occur beyond a critical…
We study the frequency and phase synchronization in two coupled identical and nonidentical neurons with channel noise. The occupation number method is used to model the neurons in the context of stochastic Hodgkin-Huxley model in which the…
This article presents a biological neural network model driven by inhomogeneous Poisson processes accounting for the intrinsic randomness of synapses. The main novelty is the introduction of local interactions: each firing neuron triggers…
Activity of inhibitory neuron with delayed feedback is considered in the framework of point stochastic processes. The neuron receives excitatory input impulses from a Poisson stream, and inhibitory impulses from the feedback line with a…