Dynamics of Coupled Oscillator Systems - Abstract
An ensemble of globally coupled oscillators can exhibit both intensive dynamics, whose dimensionality is independent of the overall dimensionality of the system, and extensive dynamics, whose dimensionality grow linearly with the system size. A stable two-cluster state is an example of the former, while a state of only incoherent oscillators is an example of the latter. In a system exhibiting both kinds of dynamics for different parameter values, the transition between the two can either take place in a single bifurcation transversal to the two-cluster manifold or through a greater number of steps. Here, we study the latter case in an ensemble of Stuart-Landau oscillators with nonlinear global coupling, where a periodic two-cluster state, stable for any ensemble size, transitions towards a fully incoherent state in a cascade of cluster-halving period-doubling bifurcations as a control parameter is varied. Inspired by the concept of information entropy, we develop a measure for quantifying the relative disorder of the intermediate states.