Desynchronization of stochastically synchronized neural populations through phase distribution control: a numerical simulation approach

Abstract

Stochastic synchrony, also known as noise-induced synchronization that leads to phase coherence, arises when a set of uncoupled neurons synchronizes to a common white noise input or other types of non-Gaussian noise. Evidence of abnormally high noise-induced synchronization, or impairment in synchronous activity, has been found in several pathologies such as epilepsy. Therefore, controlling the stochastic synchronization of neurons can have a significant effect on preventing seizures in epilepsy. The main aim of this study is to develop a fast and reliable numerical method to simulate controlling synchronization in a population of noisy and uncoupled neural oscillators. The control algorithm is based on phase reduction and uses the probability phase distribution partial differential equation to change the distribution of oscillators to the desired one. The accuracy and power consumption are two main issues that should be considered in the simulations. In this paper, a new numerical method called the generalized Lagrange Jacobi Gauss–Lobatto collocation method in space and backward-Euler scheme in time is applied to overcome the difficulties of the problem effectively. The resulting full-discrete scheme of the partial differential equation is a linear system of algebraic equations per time step which is solved via QR algorithm. Finally, the proposed algorithm is applied to various neural dynamical models with different phase response curves and investigates them in different factors such as computing time, energy consumption, and accuracy to confirm the applicability of the developed numerical method.