Standing Wave Solutions in Nonhomogeneous Delayed Synaptically Coupled Neuronal Networks (Journal of Partial Differential Equations, 2020)
The authors establish the existence and stability of standing wave solutions of a nonlinear singularly perturbed systemof integral differential equations and a nonlinear scalar integral differential equation. It will be shown that there exist six standing wave solutions (u(x,t),w(x,t))=(U(x),W(x)) to the nonlinear singularly perturbed system of integral differential equations. Similarly, there exist six standing wave solutions u(x,t)=U(x) to the nonlinear scalar integral differential equation. The main idea to establish the stability is to construct Evans functions corresponding to several associated eigenvalue problems.
Keywords: Nonhomogeneous synaptically coupled neuronal networks; standing wave solutions; existence; stability; eigenvalue problems; Evans functions