Control of sub - excitable waves in neural networks by nonlocal coupling

Transient wave forms in neural networks with diffusive and nonlocal coupling have attracted particular interest because they may mediate recruitment of healthy cortical tissue into a pathological state during migraine. To investigate this process, we use a reaction-diffusion system of inhibitor-activator type as a generic model of pathological wave propagation and set it close to bifurcation in the sub-excitable regime. We report the influence of various nonlocal connectivity schemes on wave propagation. Wave propagation can be suppressed with cross coupling inhibitor and activator for both positive and negative coupling strength K, depending on the connection length δ. The area in the parameter plane (δ,K) where this control goal is achieved resembles a Mexican-hattype network connectivity. Our results suggest that nonlocal synaptic transmission can control wave propagation, which may be of therapeutic value.