Wave fronts in neuronal fields with nonlocalpost-synaptic axonal connections and delayed nonlocal feedbackconnections - Felicia Maria G. Magpantay; Xingfu Zou (Mathematical Biosciences and Engineering)
We consider a neuronal network model with both axonal connections (in the form ofsynaptic coupling) and delayed non-local feedback connections. The kernel in thefeedback channel is assumed to be a standard non-local one, while forthe kernel in the synaptic coupling, four types are considered.The main concern is the existence of travelling wave front. By employingthe speed index function, we are able to obtain the existence of a travelling wavefront for each of these four types within certain range of model parameters.We are also able to describe how the feedback coupling strength andthe magnitude of the delay affect the wave speed. Some particular kernel functionsfor these four cases are chosen to numerically demonstrate thetheoretical results.