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An integral-differential model equation, arising from neuronal networks with both axonal and delayed nonlocal feedback connections, is considered in this paper. The kernel functions in the feedback channel we study here include not only pure excitations but also lateral inhibition. For the kernel functions in the synaptic coupling, pure excitations, lateral inhibition, the lateral excitations and more general synaptic couplings (e.g., oscillating kernel functions) are considered. The main goal of this paper is the study of the existence and uniqueness of the traveling wave front solutions. The main method we applied is the speed index functions and principle of linear superposition. © 2013 Zhang; licensee Springer.

Existence and uniqueness of wave fronts in neuronal network with nonlocal post-synaptic axonal and delayed nonlocal feedback connections