Quantitative measure of correlations: synchronization and asynchronization

Abstract

We propose a quantitative measure of correlations between coevolving dynamical systems. This measure proves to be very useful in characterizing synchronization in chaotic systems. It can distinguish between chaotic signals that are perfectly synchronized, partially synchronized, and completely asynchronized. We further illustrate the utility of this measure by using it for the analysis of the degradation of synchronization due to the variation of the parameters of the synchronizing or response systems. We find that the degradation is a smooth function of the parameter difference between the response systems and is almost symmetric about the origin.