On stability of traveling wave solutions in synaptically coupled neuronal networks

Abstract

The author is concerned with the asymptotic stability of traveling wave solutions of integral differential equations arising from synaptically coupled neuronal networks. By using complex analytic functions, he proves that there is no nonzero spectrum of some linear operator $\mathcal L$ in the region Re $\lambda \geq 0$, and $\lambda =0$ is a simple eigenvalue. By applying linearized stability criterion, he shows that the traveling wave solutions are asymptotically stable. Additionally, some explicit analytic functions are found for a scalar integral differential equation.