Stability of The Synchronization Manifold in An All-To-All Time LAG-Diffusively Coupled Oscillators

Abstract

ABSTRACT: We consider a lattice system of identical oscillators that are all coupled to one another with a diffusive coupling that has a time lag. We use the natural splitting of the system into synchronized manifold and transversal manifold to estimate the value of the time lag for which the stability of the system follows from that without a time lag. Each oscillator has a unique periodic solution that is attracting. KEYWORDS: Exponential stability, Time lag, Gronwall's Inequality.