Adaptive dynamical networks appear in various real-word systems. One of the simplest phenomenological models for investigating basic properties of adaptive networks is the system of coupled phase oscillators with adaptive couplings. In this paper, we investigate the dynamics of this system. We extend recent results on the appearance of hierarchical frequency multiclusters by investigating the e ect of the time scale separation. We show that the slow adaptation in comparison with the fast phase

more »

... ynamics is necessary for the emergence of the multiclusters and their stability. Additionally, we study the role of double antipodal clusters, which appear to be unstable for all considered parameter values. We show that such states can be observed for a relatively long time, i.e., they are metastable. A geometrical explanation for such an e ect is based on the emergence of a heteroclinic orbit. Published under license by AIP Publishing. https://doi.org/10.1063/1.5097835 Adaptive networks are characterized by the property that their connectivity can change in time, depending on the state of the network. A prominent example of adaptive networks are neuronal networks with plasticity, i.e., an adaptation of the synaptic coupling. Such an adaptation is believed to be related to learning and memory mechanisms. In other real-world systems, the adaptivity plays an important role as well. 1 This paper investigates a phenomenological model of adaptively coupled phase oscillators. The considered model is a natural extension of the Kuramoto system to the case with dynamical couplings. In particular, we review and provide new details on the self-organized emergence of multiple frequency clusters.