Complex Systems

Tools to Characterize the Correlated Nature of Collective Dynamics Download PDF

R. Vilela Mendes
CMAFcIO, Universidade de Lisboa
Faculdade de Ciências C6, 1749-016, Lisboa, Portugal

Carlos Aguirre
GNB, Escuela Politécnica Superior
Universidad Autonoma de Madrid, Campus de Cantoblanco
Ctra de Colmenar Km 16, 28049 Madrid, Spain


Synchronization, which occurs for both chaotic and nonchaotic systems, is a striking phenomenon with many practical implications for natural phenomena and technological applications. However, even before synchronization, strong correlations and complex patterns occur in the collective dynamics of natural systems. To characterize their nature is essential for understanding many phenomena in physical and social sciences as well as the perspectives to control their behavior. Because simple correlation measures are unable to characterize these collective patterns, we have developed more general methods for their detection and parametrization. The emergence of patterns of strong correlations before synchronization is illustrated in a few models. They are shown to be associated with the behavior of ergodic parameters. The models are then used as a testing ground of the new pattern characterization tools.

Keywords: correlation; synchronization; chaotic dynamics; complex patterns  

Cite this publication as:
R. Vilela Mendes and C. Aguirre, “Tools to Characterize the Correlated Nature of Collective Dynamics,” Complex Systems, 30(1), 2021 pp. 1–32.