1. Hierarchical frequency clusters in adaptive networks of phase oscillators
- Author
-
Jan Fialkowski, Rico Berner, D. V. Kasatkin, Eckehard Schöll, Serhiy Yanchuk, and Vladimir I. Nekorkin
- Subjects
adaptive dynamical network ,Phase (waves) ,General Physics and Astronomy ,Antipodal point ,FOS: Physical sciences ,Pattern Formation and Solitons (nlin.PS) ,01 natural sciences ,Stability (probability) ,010305 fluids & plasmas ,Metastability ,0103 physical sciences ,hierarchical frequency multiclusters ,ddc:530 ,Statistical physics ,010306 general physics ,Mathematical Physics ,Physics ,phase oscillators ,Applied Mathematics ,Statistical and Nonlinear Physics ,530 Physik ,Nonlinear Sciences - Pattern Formation and Solitons ,Nonlinear Sciences - Adaptation and Self-Organizing Systems ,Phase dynamics ,Heteroclinic orbit ,time scale separation ,Adaptation and Self-Organizing Systems (nlin.AO) - Abstract
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-multi-clusters by investigating the effect of the time-scale separation. We show that the slow adaptation in comparison with the fast phase dynamics is necessary for the emergence of the multi-clusters 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 effect is based on the emergence of a heteroclinic orbit., 16 pages, 8 figures
- Published
- 2019