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Circuit Synthesis and Electrical Interpretation of Synchronization in the Kuramoto Model

Kuramoto oscillator systems are well-studied models to investigate the synchronization process of coupled oscillators in a wide variety of contexts, among them neural networks. The current trend of neuromorphic systems demands electrical circuits for reasons of efficiency, low costs, and high speed. The goal of this work is to study the Kuramoto model with arbitrary coupling structure from a circuit theoretical perspective. For this reason, we synthesize an ideal electrical circuit based on the Kuramoto model which enables an electrical interpretation of its synchronization behavior. Because of the knowledge of voltage, current and power flows in (ideal) electrical devices, circuit synthesis in general can offer perspectives and interpretation that might not be attainable from system theory. We therefore see the structured approach of the synthesis and its electrical interpretation of the well-known Kuramoto model as a general procedure that will increase insights and diversify understanding on neural networks. To achieve this, we utilize the wave digital concept here which offers an especially intuitive view on power flow.