Stability of traveling wave in a PDE approximation of coupled arrays of Chua's circuit

Abstract

Coupled arrays of Chua's circuit have been studied extensively. The system admits traveling front, back, pulse as well as periodic and chaotic waves. However, the stability problem of these waves has rarely been investigated. In this paper, we consider the PDE approximation of the system and prove for the PDE that the traveling back is nonlinearly stable. The question of stability can be reduced to an eigenvalue problem in R4. The Evans function method is applied, along with the geometric singular perturbation theory and the smooth linearization.