An efficient space-splitting method for simulating brain neurons by neuronal synchronization to control epileptic activity

TL;DR: In this study, the generalized Lagrange Jacobi Gauss–Lobatto collocation method combined with Trotter operator splitting technique is employed, which allows us to decouple the nonlinear partial differential equations of neural network models into independent linear algebraic equations of very small dimensions.

Abstract: Controlling synchronization of neural networks in brain activity is an important issue in neurodevelopmental disorders such as epileptic seizures In this paper, we propose an efficient numerical method to simulate nonlinear spatio-temporal neural dynamic models and their synchronizations In this study, the generalized Lagrange Jacobi Gauss–Lobatto collocation method combined with Trotter operator splitting technique is employed This method allows us to decouple the nonlinear partial differential equations of neural network models into independent linear algebraic equations of very small dimensions Moreover, we examine different test cases to indicate the advantages of the proposed method in accuracy, computational cost, and complexity It is shown that the computational complexity of the proposed method is much smaller than the complexity of pure spectral method Finally, A GPU implementation is applied on the two dimensional models to accelerate the time consuming simulations