Abstract
In this work, we propose to use the distance correlation ([Formula: see text]) and the Euclidian distance ([Formula: see text]) as powerful quantifiers to describe correlation and synchronization in spatially extended systems. As examples, we use the coupled Kuramoto oscillator model and coupled map lattices to study chimera states. Results for [Formula: see text] and [Formula: see text] are compared and discussed in terms of recurrence plots, local synchronization order parameter, local recurrence rate, and local [Formula: see text] rate. The existence of correlations between desynchronized states, not visible in usual recurrence plots, becomes evident when using [Formula: see text] and [Formula: see text]. Since correlation is a broader concept than synchronization, the proposed quantifiers amplify the characterization, description and possible application of spatially extended systems.
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