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This paper considers a conjecture-based distributed learning approach that enables autonomous nodes to independently optimize their transmission probabilities in random access networks. We model the interaction among multiple…
We study the global dynamics of integrate and fire neural networks composed of an arbitrary number of identical neurons interacting by inhibition and excitation. We prove that if the interactions are strong enough, then the support of the…
We present a detailed analysis of the dynamical regimes observed in a balanced network of identical Quadratic Integrate-and-Fire (QIF) neurons with a sparse connectivity for homogeneous and heterogeneous in-degree distribution. Depending on…
Under suitable assumptions, the dynamic behaviour of a chemical reaction network is governed by an autonomous set of polynomial ordinary differential equations over continuous variables representing the concentrations of the reactant…
For large fully connected neuron networks, we study the dynamics of homogenous assemblies of interacting neurons described by time elapsed models. Under general assumptions on the firing rate which include the ones made in previous works…
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…
Even a single neuron may be able to produce significant lognormal features in its firing statistics due to noise in the charging ion current. A mathematical scheme introduced in advanced nanotechnology is relevant for the analysis of this…
A novel approach to moment closure problem is used to derive low dimensional laws for the dynamics of the moments of the membrane potential distribution in a population of spiking neurons. Using spectral expansion of the density equation we…
Coupling frequently enhances noise-induced coherence and synchronization in interacting nonlinear systems, but it does so separately. In principle collective stochastic coherence and synchronizability are incompatible phenomena, since…
A central question in neuroscience is to understand how noisy firing patterns are used to transmit information. Because neural spiking is noisy, spiking patterns are often quantified via pairwise correlations, or the probability that two…
Networked nonlinear systems present a variety of emergent phenomena as a result of the mutual interactions between their units. An interesting feature of these systems is the presence of stable periodic behavior even when each unit…
Random networks of symmetrically coupled, excitable elements can self-organize into coherently oscillating states if the networks contain loops (indeed loops are abundant in random networks) and if the initial conditions are sufficiently…
Mathematical models for systems of interacting agents using simple local rules have been proposed and shown to exhibit emergent swarming behavior. Most of these models are constructed by intuition or manual observations of real phenomena,…
The understanding of emergent collective phenomena in natural and social systems has driven the interest of scientists from different disciplines during decades. Among these phenomena, the synchronization of a set of interacting individuals…
It is known that an identical delay in all transmission lines can destabilize macroscopic stationarity of a neural network, causing oscillation or chaos. We analyze the collective dynamics of a network whose intra-transmission delays are…
The manner in which groups of neurons represent events in the external world is fundamental to neuroscience. Here, we analyze the population code of the retina during naturalistic stimulation and show that the information conveyed by…
We report a transition from asynchronous to oscillatory behaviour in balanced inhibitory networks for class I and II neurons with instantaneous synapses. Collective oscillations emerge for sufficiently connected networks. Their origin is…
We investigate the dynamics of a neural network where each neuron evolves according to the combined effects of deterministic integrate-and-fire dynamics and purely inhibitory coupling with K randomly-chosen "neighbors". The inhibition…
Network coherence generally refers to the emergence of simple aggregated dynamical behaviours, despite heterogeneity in the dynamics of the subsystems that constitute the network. In this paper, we develop a general frequency domain…
We study two delay-coupled FitzHugh-Nagumo systems, introducing a mismatch between the delay times, as the simplest representation of interacting neurons. We demonstrate that the presence of delays can cause periodic oscillations which…