Berlin 2018 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 73: Poster: Networks, Chimera, Energy Systems

DY 73.7: Poster

Thursday, March 15, 2018, 15:30–18:00, Poster A

Phase balancing in the Kuramoto model on small networks — •Franz Kaiser and Karen Alim — Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany

Weakly interacting oscillators play a crucial role for transport and timing along a broad range of systems, from biological systems to powergrids and control of autonomous vehicles. In many oscillator networks the interaction is constrained by boundary effects or conservation laws. Among theoretical models used for coupled oscillators on networks, the Kuramoto model stands out due to its tractability and applicability. While research regarding the Kuramoto model has mainly focused on synchronization phenomena, so called phase balanced states are important for constrained systems. An example occurring in nature are the periodically contracting tubes of the network-shaped organism Physarum polycephalum. Here, conservation of fluid volume enclosed within the tubular network is prohibiting synchronized contractions. However, very little is known on the structure of balanced states and the networks stabilizing these in Kuramoto’s model. Here, we investigate a certain class of networks in which balanced states turn out to be stable and compare them to networks formed by P. polycephalum. The structure of this class of networks is highly symmetric, while the underlying graphs are in general neither circulant nor regular. We derive analytical results correctly characterizing the scaling of phase balanced states with increasing number of nodes in a subclass of the networks found. Our findings point out that network architectures that differ from circulant graphs may well support stable phase balanced states.