EVANS FUNCTIONS AND NONLINEAR STABILITY OF TRAVELING WAVES IN NEURONAL NETWORK MODELS.

Modeling networks of synaptically coupled neurons often leads to systems of integro-differential equations. Particularly interesting solutions in this context are traveling waves. We prove here that spectral stability of traveling waves implies their nonlinear stability in appropriate function spaces, and compare several recent Evans-function constructions that are useful tools when analyzing spectral stability. [ABSTRACT FROM AUTHOR]