Numerical simulation of reaction-diffusion neural dynamics models and their synchronization/desynchronization: Application to epileptic seizures

摘要

Cognitive disorders especially epilepsy are closely linked with synchronization/desynchronization of neurons in the brain. In this paper, the dynamical modeling and behavior analysis of a FitzHugh-Nagumo neuron and also synchronization control of a network of FitzHugh-Nagumo neurons which promise the understanding of cognitive processing, are studied. To numerically simulate these models and in order to overcome their difficulties such as computational complexity, multi-dimensionality, non-linearity, having large spatial and temporal domains and also having a discrete initial data, we propose the use of a strongly meshless technique based on Wendland compactly supported radial basis function in conjunction with an operator splitting algorithm. The main advantage of the proposed algorithm is its computational complexity (for example O(N-x1(3)+ N-x2(3) ) of the inversion of all matrices) which is much lower than the complexity of pure radial basis functions method (O(N-x1(3)+ N-x2(3)) of the inversion of matrices). Numerical experiments are presented showing that the proposed approaches are extremely accurate and fast. (C) 2019 Elsevier Ltd. All rights reserved.