Detecting correlations in desynchronized chaotic chimera states. (English) Zbl 1541.37093
Summary: In this work, we propose to use the distance correlation \((DC)\) and the Euclidian distance \((ED)\) 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 \(DC\) and \(ED\) are compared and discussed in terms of recurrence plots, local synchronization order parameter, local recurrence rate, and local \(DC\) rate. The existence of correlations between desynchronized states, not visible in usual recurrence plots, becomes evident when using \(DC\) and \(ED\). Since correlation is a broader concept than synchronization, the proposed quantifiers amplify the characterization, description and possible application of spatially extended systems.
MSC:
| 37M25 | Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.) |
| 37M05 | Simulation of dynamical systems |
| 37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
| 34C15 | Nonlinear oscillations and coupled oscillators for ordinary differential equations |
| 65P20 | Numerical chaos |
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