We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Existence of Wave Front Solutions of an Integral Differential Equation in Nonlinear Nonlocal Neuronal Network.
- Authors
Lijun Zhang; Linghai Zhang; Jie Yuan; Khalique, C. M.
- Abstract
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.
- Subjects
TRAVELING waves (Physics); NONLINEAR network analysis; INTEGRALS; KERNEL functions; DIFFERENTIAL equations; NUMERICAL analysis; MATHEMATICAL models
- Publication
Abstract & Applied Analysis, 2014, p1
- ISSN
1085-3375
- Publication type
Article
- DOI
10.1155/2014/753614