Related papers: Metastability for systems of interacting neurons

The brain's activity is characterized by the interaction of a very large number of neurons that are strongly affected by noise. However, signals often arise at macroscopic scales integrating the effect of many neurons into a reliable…

We study a network of spiking neurons with heterogeneous excitabilities connected via inhibitory delayed pulses. For globally coupled systems the increase of the inhibitory coupling reduces the number of firing neurons by following a Winner…

The problem of metastability for a stochastic dynamics with a parallel updating rule is addressed in the Freidlin--Wentzel regime, namely, finite volume, small magnetic field, and small temperature. The model is characterized by the…

Zero-range processes with decreasing jump rates are known to exhibit condensation, where a finite fraction of all particles concentrates on a single lattice site when the total density exceeds a critical value. We study such a process on a…

Local networks of neurons are nonlinear systems driven by synaptic currents elicited by its own spiking activity and the input received from other brain areas. Synaptic currents are well approximated by correlated Gaussian noise. Besides,…

This paper continues the study of metastable behaviour in disordered mean field models initiated in [2], [3]. We consider the generalized Hopfield model with finitely many independent patterns $\xi_1,...,\xi_p$ where the patterns have…

Cortical neurons include many sub-cellular processes, operating at multiple timescales, which may affect their response to stimulation through non-linear and stochastic interaction with ion channels and ionic concentrations. Since new…

The characterization of network and biophysical properties from neural spiking activity is an important goal in neuroscience. A framework that provides unbiased inference on causal synaptic interaction and single neural properties has been…

We study small random perturbations by additive space-time white noise of a reaction-diffusion equation with a unique stable equilibrium and solutions which blow up in finite time. We show that for initial data in the domain of attraction…

Developing networks of neural systems can exhibit spontaneous, synchronous activities called neural bursts, which can be important in the organization of functional neural circuits. Before the network matures, the activity level of a burst…

We examine the stability and qualitative dynamics of stochastic neuronal networks specified as multivariate nonlinear Hawkes processes and related point-process generalized linear models that incorporate both auto- and cross-history…

We study a neural network model of interacting stochastic discrete two--state cellular automata on a regular lattice. The system is externally tuned to a critical point which varies with the degree of stochasticity (or the effective…

We study the statistical physics of a surprising phenomenon arising in large networks of excitable elements in response to noise: while at low noise, solutions remain in the vicinity of the resting state and large-noise solutions show…

We study thermal instability in NbN superconducting stripline resonators. The system exhibits extreme nonlinearity near a bifurcation, which separates a monostable zone and an astable one. The lifetime of the metastable state, which is…

Analysing biological spiking neural network models with synaptic plasticity has proven to be challenging both theoretically and numerically. In a network with N all-to-all connected neurons, the number of synaptic connections is on the…

We study associative memory neural networks of the Hodgkin-Huxley type of spiking neurons in which multiple periodic spatio-temporal patterns of spike timing are memorized as limit-cycle-type attractors. In encoding the spatio-temporal…

We study a model of interacting neurons. The structure of this neural system is composed of two layers of neurons such that the neurons of the first layer send their spikes to the neurons of the second one: if $N$ is the number of neurons…

We study complex networks of stochastic two-state units. Our aim is to model discrete stochastic excitable dynamics with a rest and an excited state. Both states are assumed to possess different waiting time distributions. The rest state is…

Stochastic chemical reaction or population dynamics in finite systems often terminates in an absorbing state. Yet in large spatially extended systems, the time to reach species extinction (or fixation) becomes exceedingly long. Tuning…

Spontaneous brain activity in the absence of external stimuli is not random but contains complex dynamical structures such as neuronal avalanches with power-law duration and size distributions. These experimental observations have been…