Isochronal synchronization in complex networks - The Lyapunov-Krasovskii theorem and stability in the network parameter space

Isochronal synchronization is a unique phenomenon in which physically distant oscillators wired together relax into zero-lag synchronous behavior over time. Such behavior is observed in natural processes and, recently, has been considered for promising applications in communication. Towards technological development of devices that explore isochronal sync, stability issues of the phenomenon need to be considered, both in the context of a pair or a network of coupled oscillators. This study concerns such stability issues by using the Lyapunov-Krasovskii theorem to propose a framework to study synchronization stability by using accessible parameters of the network coupling setup. As a result, relations between stability and network parameters are unveiled and the comprehension of roads leading to stability is enhanced.