The use of space-splitting RBF-FD technique to simulate the controlled synchronization of neural networks arising from brain activity modeling in epileptic seizures

This paper investigates the behavior and synchronization of a network of reaction–diffusion neural dynamics models using a highly efficient numerical method. In fact, the dynamical modeling, behavior analysis and controlled synchronization of a network of FitzHugh–Nagumo (FHN) neurons which promising the understanding of cognitive processing are studied by considering the unidirectional gap junctions in the medium between two distant neurons. In this study, radial basis function generated finite differences (RBF-FD) technique is employed in conjunction with a suitable operator splitting technique, which allows us to decouple the nonlinear partial differential equations of neural network models into independent linear algebraic equations of very small dimensions. The most important advantages of the proposed method can be high accuracy and high speed, very low computational complexity, and the sparsity property of the matrix of the coefficients derived from its linear systems, which distinguish the proposed method from other methods. The analyses and numerical results presented totally confirm these claims.

Finite difference, Radial basis function, Fitzhugh–Nagumo, Operator splitting, Synchronization, Epilepsy