Discontinuous Galerkin approximation for excitatory-inhibitory networks with delay and refractory periods

Abstract

In this study, we consider the network of noisy leaky integrate-and-fire (NNLIF) model, which governs by a second-order nonlinear time-dependent partial differential equation (PDE). This equation uses the probability density approach to describe the behavior of neurons with refractory states and the transmission delays. A numerical approximation based on the discontinuous Galerkin (DG) method is used for the spatial discretization with the analysis of stability. The strong stability-preserving explicit Runge–Kutta (SSPERK) method is performed for the temporal discretization. Finally, some test examples and numerical simulations are given to examine the behavior of the solution. The execution of the constructed scheme is measured by the quantitative comparison with the existing finite difference technique, namely weighted essentially nonoscillatory (WENO) scheme.