Investigating the Interplay of Resonance and Coupling in Neural Synchronization: A Comparative Study of Kuramoto Models

Abstract

Richard Murdoch Montgomery

Understanding the dynamics of neural synchronization is vital for decoding the complex behavior of neural systems. One of the commonly employed mathematical frameworks for studying neural synchronization is the Kuramoto model. While coupling has been extensively studied in the context of synchronization, the role of resonance remains relatively unexplored. In this study, we investigate the interplay between resonance and coupling in the Kuramoto model by in- troducing an external driving force. The external driving force represents the resonant conditions, modeled as a sinu- soidal function with specific amplitude and frequency. Our comparative analysis covers scenarios with and without the external driving force to reveal how resonance interacts with the inherent coupling of oscillators. We find that resonance can either amplify or dampen the synchronization, depending on the strength of coupling and natural frequencies of oscillators. This insight has implications for understanding not only neural systems but also other complex, oscillatory systems. The study opens new avenues for exploring the multi-faceted dynamics of coupled oscillators in the presence of external resonant forces.

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