Assessing synchronizability provided by coupling variable from the algebraic structure of dynamical systems.

Abstract

Synchronization is a very generic phenomenon which can be encountered in a large variety of coupled dynamical systems. Being able to synchronize chaotic systems is strongly dependent on the nature of their coupling. Few attempts to explain such a dependency using observability and/or controllability were not fully satisfactory and synchronizability yet remained unexplained. Synchronizability can be defined as the range of coupling parameter values for which two nearly identical systems are fully synchronized. Our objective is here to investigate whether synchronizability can be related to the main rotation necessarily required for structuring any type of attractor, that is, whether synchronizability is significantly improved when the coupling variable is one of the variables involved in the main rotation. We thus propose a semianalytic procedure from a single isolated system to discard the worst variable for fully synchronizing two (nearly) identical copies of that system.