Dynamics, correlation scaling, and synchronization behavior in rings of delay-coupled oscillators

We study the dynamics of unidirectionally delay-coupled nonlinear oscillators. Cascading them within a ring of fixed total propagation delay, we demonstrate simple scaling behavior of correlation properties. In fact, the correlation properties of a ring with N elements can be deduced from the autocorrelation of the single delayed feedback system. Coupling a ring element to a chain of unidirectionally coupled identical oscillators, we achieve complete synchronization between elements of chain and ring, evidencing generalized synchronization among the other elements, even if uncorrelated.