A spatial-temporal model for the propagation of abnormal oscillations in a 2D excitable neural tissue

A 2D spatial-temporal partial differential equation (PDE) is developed to study the propagation of abnormal oscillations in a neural network that is composed of excitable neurons. These neurons are coupled via gap junctions. Combining with the multi-step algorithm to solve the nonlinear ordinary differential equations in the model, the implicit scheme of the finite differential method in the time domain is utilized to solve the PDE, and the successive over-relaxation method is utilized in the computation of the large-scale sparse equation. The Lyapunov exponent is applied to the analysis for chaos in the propagation. Numerical results show that abnormal oscillations can propagate when the coupling strength of the gap junction is large enough, and the nonlinearity of activities in the network affected by the propagation increases with the gap junction strength. The theoretical work can be helpful, to a certain extent, in understanding turbulence in the propagation of abnormal oscillations in a 2D neural tissue. It may thus be helpful for understanding the pathological mechanisms of diseases such as epilepsy.