Related papers: Weak-noise-induced transitions with inhibition and…

In various neurological disorders spatio-temporal excitation patterns constitute examples of excitable behavior emerging from pathological pathways. During migraine, seizure, and stroke an initially localized pathological state can…

In this paper we study noise-induced bistability in a specific circuit with many biological implications, namely a single-step enzymatic cycle described by Michaelis Menten equations with quasi-steady state assumption. We study the system…

We consider spatially localized spiking activity patterns, so-called bumps, in ensembles of bistable spiking oscillators. The bistability consists in the coexistence of self-sustained spiking dynamics and quiescent steady-state regime. We…

Cortical neurons are bistable; as a consequence their local field potentials can fluctuate between quiescent and active states, generating slow 0.5-2 Hz oscillations which are widely known as transitions between Up and Down States. Despite…

We demonstrate that waves in distinct layers of a neuronal network can become phase-locked by common spatiotemporal noise. This phenomenon is studied for stationary bumps, traveling waves, and breathers. A weak noise expansion is used to…

We examine the effects of pure additive noise on spatially extended systems with quadratic nonlinearities. We develop a general multiscale theory for such systems and apply it to the Kuramoto-Sivashinsky equation as a case study. We first…

We present a simple analytical tool which gives an approximate insight into the stationary behavior of nonlinear systems undergoing the influence of a weak and rapid noise from one dominating source, e.g. the kinetic equations describing a…

According to the conventional approach to model neural ensembles the extracellular environment has fixed ionic concentrations. However, in many cases the extracellular concentration of potassium ions can not be regarded as constant. That…

We analyse the effect of intrinsic fluctuations on the properties of bistable stochastic systems with time scale separation operating under1 quasi-steady state conditions. We first formulate a stochastic generalisation of the quasi-steady…

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…

A recent study on the effect of colored driving noise on the escape from a metastable state derives an analytic expression of the transfer function of the leaky integrate-and-fire neuron model subject to colored noise. Here we present an…

Epilepsy is one of the most common neurological disorders globally, affecting millions of individuals. Despite significant advancements, the precise mechanisms underlying this condition remain largely unknown, making accurately predicting…

We measure the spectral densities of fluctuations of an underdamped nonlinear micromechanical oscillator. By applying a sufficiently large periodic excitation, two stable dynamical states are obtained within a particular range of driving…

In this article, we study the FitzHugh-Nagumo $(1,1)$--fast-slow system where the vector fields associated to the slow/fast equations come from the reduction of the Hodgin-Huxley model for the nerve impulse. After deriving dynamical…

Subthreshold oscillations in neurons are those oscillations which do not attain the critical value of the membrane's voltage needed for triggering an action potential (a spike). Their contribution to the forming of action potentials in…

The influence of time delay in systems of two coupled excitable neurons is studied in the framework of the FitzHugh-Nagumo model. Time-delay can occur in the coupling between neurons or in a self-feedback loop. The stochastic…

We study the stable phases of an attractor neural network model, with binary units, for hippocampal place cells encoding 1D or 2D spatial maps or environments. Using statistical mechanics tools we show that, below critical values for the…

It has been proposed that neural noise in the cortex arises from chaotic dynamics in the balanced state: in this model of cortical dynamics, the excitatory and inhibitory inputs to each neuron approximately cancel, and activity is driven by…

A wave front and a wave back that spontaneously connect two hyperbolic equilibria, known as a heteroclinic wave loop, give rise to periodic waves with arbitrarily large spatial periods through the heteroclinic bifurcation. The nonlinear…

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…