Decentralized coupling-when-needed strategy for the synchronization of networked oscillators with delays

A large literature has investigated the stability of the synchronous solution over a chaotic or periodic time evolution, for an arbitrary network of coupled oscillators. Delays may affect the dynamics of an uncoupled oscillator or node-to-node coupling. An important result is that in the presence of small perturbations about the synchronous solution there is a maximum Lyapunov exponent that determines asymptotic stability. However, different regions of a chaotic or periodic attractor have different transverse reactivities, which measure the transient growth of the norm of the perturbations. Knowledge about the reactive characterization of an attractor can be used to implement a control action only when needed and achieve synchronization efficiently, i.e., by reducing the amount of control used. In this paper we consider arbitrary networks of coupled lasers in the presence of self-feedback delay and laser-to-laser communication delays and successfully implement an efficient synchronization strategy, based on knowledge about the reactivity of the attractor.