Correlation and collective behaviour in Adler-type locally coupled oscillators at the edge of chaos

Abstract: Dynamical systems can be analyzed as computational devices capable of performing information processing. In coupled oscillators, enlarged capabilities are expected when the set of units is formed by subsets with collective behaviour within them but weak correlation between the subsets. A system of non-linear oscillators weakly coupled in the phase approximation is studied. The informational distance maps show different regimes of collective behaviour, ranging from independent, local, and global, as the control parameters of the system are changed. This rich set of behaviours happens despite the simple nature of the model used. Complex hierarchies between oscillators can be identified near the edge of chaos region in the informational distance dendrograms. We identify the emergence of local collective regimes, further corroborated by the spatiotemporal maps. Correlation diagrams also exhibit non-trivial dependence for the system at the edge of chaos.