On a conjecture regarding the synchronization in an array of linearly coupled dynamical systems

摘要

In this letter, we give supporting evidence for a conjecture regarding the amount of coupling needed to synchronize an array of linearly coupled dynamical systems. Roughly speaking, the conjecture says that the coupling needed to synchronize an array of coupled systems is inversely proportional to the nonzero eigenvalue of the coupling graph that is smallest in magnitude. The conjecture implies that the coupling needed to synchronize an array can be derived from the coupling topology and the coupling needed to synchronize two coupled dynamical systems.