TY - JOUR A2 - Yuan, Sanling AU - Zhang, Lijun AU - Zhang, Linghai AU - Yuan, Jie AU - Khalique, C. M. PY - 2014 DA - 2014/04/07 TI - Existence of Wave Front Solutions of an Integral Differential Equation in Nonlinear Nonlocal Neuronal Network SP - 753614 VL - 2014 AB - An integral-differential model equation arising from neuronal networks with very general kernel functions is considered in this paper. The kernel functions we study here include pure excitations, lateral inhibition, lateral excitations, and more general synaptic couplings (e.g., oscillating kernel functions). The main goal of this paper is to prove the existence and uniqueness of the traveling wave front solutions. The main idea we apply here is to reduce the nonlinear integral-differential equation into a solvable differential equation and test whether the solution we get is really a wave front solution of the model equation. SN - 1085-3375 UR - https://doi.org/10.1155/2014/753614 DO - 10.1155/2014/753614 JF - Abstract and Applied Analysis PB - Hindawi Publishing Corporation KW - ER -