Dynamical behavior of reaction–diffusion neural networks and their synchronization arising in modeling epileptic seizure: A numerical simulation study

Abstract

Excessive synchronizations of neurons in the brain networks can be a reason for some episodic disorders such as epilepsy. In this paper, we simulate neural dynamic models and their synchronizations numerically by a new numerical algorithm. In order to overcome the complexity of the problem, a suitable combination of the Legendre spectral element method and operator splitting technique is proposed to convert a complex system of partial differential equations into sparse linear algebraic systems. The simulations are explored in different aspects such as accuracy, computing the wavefront and angular speeds, computing time, the condition number of obtained algebraic systems to demonstrate the proposed scheme effectiveness. The numerical simulations and comparisons confirm the method is suitable in terms of accuracy and speed.