Long-time behavior of stochastically perturbed neuronal networks
نویسندگان
چکیده
Our investigation is specially motivated by the stochastic version of a common model of potential spread in a dendritic tree. We do not assume the noise in the junction points to be Markovian. In fact, we allow for long-range dependence in time of the stochastic perturbation. This leads to an abstract formulation in terms of a stochastic diffusion with dynamic boundary conditions, featuring fractional Brownian motion. We prove results on existence, uniqueness and asymptotics of weak and strong solutions to such a stochastic differential equation.
منابع مشابه
Large Fluctuations in Stochastically Perturbed Nonlinear Systems: Applications in Computing
Nonlinear dynamical systems often display complex behavior. In this lecture I shall review the behavior of stochastically perturbed dynamical systems, which is a field of its own. I shall use this as an opportunity to discuss applications to computer science, though applications to statistical physics, chemical physics, and elsewhere in the sciences are also numerous. If a deterministic dynamic...
متن کاملExistence and Stability of Square-mean Almost Periodic Solutions to a Spatially Extended Neural Network with Impulsive Noise
Our work is concerned with a neural network with n nodes, where the activity of the k-th cell depends on external, stochastic inputs as well as the coupling generated by the activity of the adjacent cells, transmitted through a diffusion process in the network. This paper aims to throw some light on time-varying, stochastically perturbed, neuronal networks. We show that when the coefficients os...
متن کاملPath to Stochastic Stability: Comparative Analysis of Stochastic Learning Dynamics in Games
Stochastic stability is a popular solution concept for stochastic learning dynamics in games. However, a critical limitation of this solution concept is its inability to distinguish between different learning rules that lead to the same steadystate behavior. We address this limitation for the first time and develop a framework for the comparative analysis of stochastic learning dynamics with di...
متن کاملSpontaneous formation of synchronization clusters in homogenous neuronal ensembles induced by noise and interaction delays.
The spontaneous formation of clusters of synchronized spiking in a structureless ensemble of equal stochastically perturbed excitable neurons with delayed coupling is demonstrated for the first time. The effect is a consequence of a subtle interplay between interaction delays, noise, and the excitable character of a single neuron. The dependence of the cluster properties on the time lag, noise ...
متن کاملSynchronization in an array of linearly stochastically coupled networks with time delays
In this paper, the complete synchronization problem is investigated in an array of linearly stochastically coupled identical networks with time delays. The stochastic coupling term, which can reflect a more realistic dynamical behavior of coupled systems in practice, is introduced to model a coupled system, and the influence from the stochastic noises on the array of coupled delayed neural netw...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008