Related papers: Delay-induced stochastic bursting in excitable noi…
We study a stochastic system of interacting neurons and its metastable properties. The system consists of $N$ neurons, each spiking randomly with rate depending on its membrane potential. At its spiking time, the neuron potential is reset…
Following our recent study (S. Kundu and M. Acharyya, International Journal of Modern Physics C, 35 (2024) 2450094), we have introduced stochasticity (random noise) in the Fairen-Velarde deterministic differential equations. The role of…
We consider a reaction-diffusion equation on a network subjected to dynamic boundary conditions, with time delayed behaviour, also allowing for multiplicative Gaussian noise perturbations. Exploiting semigroup theory, we rewrite the…
We review the mathematical formalism underlying the modelling of stochasticity in biological systems. Beginning with a description of the system in terms of its basic constituents, we derive the mesoscopic equations governing the dynamics…
In this paper, we study a class of self-exciting point processes. The intensity of the point process has a nonlinear dependence on the past history and time. When a new jump occurs, the intensity increases and we expect more jumps to come.…
This paper is concerned with stochastic reaction-diffusion kinetics governed by the reaction-diffusion master equation. Specifically, the primary goal of this paper is to provide a mechanistic basis of Turing pattern formation that is…
We develop an effective description of noise-induced oscillations based on deterministic phase dynamics. The phase equation is constructed to exhibit correct frequency and distribution density of noise-induced oscillations. In the simplest…
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…
Motivated by studies of indirect measurements in quantum mechanics, we investigate stochastic differential equations with a fixed point subject to an additional infinitesimal repulsive perturbation. We conjecture, and prove for an important…
We propose a discrete time dynamical system (a map) as phenomenological model of excitable and spiking-bursting neurons. The model is a discontinuous two-dimensional map. We find condition under which this map has an invariant region on the…
We study the joint dynamics of membrane potential and time since the last spike in a population of integrate-and-fire neurons using a population density framework. This leads to a two-dimensional Fokker-Planck equation that captures the…
This paper continues the study of [11, 13] for stationary solutions of stochastic linear retarded functional differential equations with the emphasis on delays which appear in those terms including spatial partial derivatives. As a…
The stochastic FitzHugh-Nagumo model with time delayed-feedback is often studied in excitable regime to demonstrate the time-delayed control of coherence resonance. Here, we show that the impact of time-delayed feedback in the…
Stochasticity in gene expression can give rise to fluctuations in protein levels and lead to phenotypic variation across a population of genetically identical cells. Recent experiments indicate that bursting and feedback mechanisms play…
We investigate the effects of heterogeneous delays in the coupling of two excitable neural systems. Depending upon the coupling strengths and the time delays in the mutual and self-coupling, the compound system exhibits different types of…
One of the major challenges in neuroscience is to determine how noise that is present at the molecular and cellular levels affects dynamics and information processing at the macroscopic level of synaptically coupled neuronal populations.…
This article present a continuous cascade model of volatility formulated as a stochastic differential equation. Two independent Brownian motions are introduced as random sources triggering the volatility cascade. One multiplicatively…
We consider stochastic dynamics of a particle on a plane in presence of two noises and a confining parabolic potential - an analog of the experimentally-relevant Brownian Gyrator (BG) model. In contrast to the standard BG model, we suppose…
In this paper we develop a perturbation method to predict the rate of occurrence of rare events for singularly perturbed stochastic systems using a probability density function approach. In contrast to a stochastic normal form approach, we…
Stochastic processes with multiplicative noise have been studied independently in several different contexts over the past decades. We focus on the regime, found for a generic set of control parameters, in which stochastic processes with…