Aachen 2019 – wissenschaftliches Programm
AKPIK 2.7: Vortrag
Dienstag, 26. März 2019, 17:00–17:10, H10
Circuit Synthesis of the Kuramoto Model and Electrical Interpretation of its Synchronization Condition — Karlheinz Ochs1, •Dennis Michaelis1, Julian Roggendorf1, Petro Feketa2, Alexander Schaum2, and Thomas Meuerer2 — 1Ruhr-University Bochum, Bochum, Germany — 2Christian-Albrechts-Universität zu Kiel, Kiel, Germany
The authors present a circuit synthesis of the well-known Kuramoto model. It is a fundamental setup which consists of non-linearly coupled oscillators, making it an interesting subject in the context of synchronization. The circuit synthesis consists of synthesizing the oscillators first and then deriving a circuit of a general resistive interconnection network. Additionally, the standard Kuramoto model implies a strongly connected interconnection network which we generalize to an arbitrary connection topology. Based on the resulting electrical circuit, a sufficient synchronization condition is derived that coincides with the system-theoretic synchronization condition that is known from the literature. By interpreting the electrical quantities, simulation results explain in detail how the different kinds of synchronization known to be present in the Kuramoto model (zero-sum, anti-phase, complete synchronization) can occur. A simulation scenario focuses on an auxiliary oscillator aiding the transition from an anti-phase configuration to a state of complete synchronization. The structured approach of the synthesis and its electrical interpretation is seen as a general procedure to derive perspectives on neural networks, which typically require circuits for reasons of efficiency, low costs and high speed.