Chaotic cluster itinerancy and hierarchical cluster trees in electrochemical experiments

摘要

Coupling of chaotic oscillators can lead to dynamical clustering where elements spontaneously differentiate into groups of synchronized oscillators. When the clusters are stable the system remains in a stationary state. However, the number of clusters can also vary with time and thus the system alternates between high- and low-dimensional states as the number of clusters varies. The formation of dynamical clusters has been used to explain biological and ecological networks. Itinerancy among states of different complexity has relevance to the interpretation of dynamic neural activities. Here we present results on spontaneous dynamical differentiation, or clustering, in a model experimental system, viz., a set of globally coupled chaotic electrochemical oscillators. The system, as many experimental systems, has a certain amount of heterogeneity and noise. The clustering is followed as a function of time. We show the existence of both simple and complex transitions among cluster states in which the system itinerates between two-cluster states and many-cluster states.