Nonlocal Coupling Effects on a Network of Neurons

Many biological systems such as groups of heart cells and neural tissue can exhibit excitatory or oscillatory behavior. In this project, we look at the particular example of neural tissue. We use the Wiener-Rosenblueth (WR) and FitzHugh-Nagumo (FHN) models to study how nonlocal coupling affects pattern formation in excitatory and oscillatory systems, respectively. We model a network of neurons with a square grid, and apply the WR and FHN equations to it. In excitatory systems, we will explore how nonlocal coupling affects spiral wave formation. In oscillatory systems, we will determine how Levy-type coupling and a network structure formed of two layers affects the formation of chimera patterns.