Controllability and synchronizability: Are they related?

• We investigate if controllability coefficients correlate with measures of synchronization performance.
• We use two toy-models: the Rössler and cord systems.
• We considered four different synchronization schemes.
• We did not find any general relation between controllability coefficients and synchronizability for the investigated systems.

In the two last decades the concept of observability has been formally linked to that of embedding in the context of nonlinear dynamics. Such a concept has been shown to play an important role in global modeling, data analysis and filtering, to mention a few examples. Preliminary results suggested that observability, at least in some cases, has some influence in synchronization problems. Could the dual concept of controllability also be important in such problems? In the context of synchronization, in general, the role played by controllability properties may not be as relevant as observability is for data analysis. In this work we compute controllability coefficients analogous to the observability ones, now established in the literature, and evaluate their importance in synchronization problems. Two benchmarks have been used in the simulations: the Rössler and the cord systems. The following schemes were investigated: synchronization to external sinusoidal force, complete replacement, uni- and bi-directional coupling of identical oscillators. The results discussed in this work show that controllability and synchronizability are not related in general.