Relaxation timescales in Kuramoto Model

Sinha, Abhisek (2022) Relaxation timescales in Kuramoto Model. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS dissertation of Abhisek Sinha (17MS065)) 17MS065_Thesis_file.pdf - Submitted Version Restricted to Repository staff only Download (3MB)

Abstract

Synchronisation is a widely seen and studied phenomenon. It has been realised in an array of lasers, superconducting Josephson junctions, pacemakers cells in the heart, flashing of the fireflies and many more systems. It has also been studied vastly to explore the effects of different types of coupling, the existence of critical coupling strength, and the stability of the synchronised state, to name a few. In this project, we are trying to search for universal features in the relaxation timescales of the synchronisation process. We want to answer questions like how these timescales are affected by coupling strengths and noise strengths and if there is an optimal regime due to the competition of these two effects. To study this, the paradigm of the Kuramoto model is chosen. We start with the simplest case of the global coupled Kuramoto model, focusing more on the temporal dynamics of the system using Ott-Antonsen ansatz. Then we shift our focus to finding out the first passage time distribution (FPT) of the system. We numerically show that the FPT distribution is Gumbel (Type-I Extreme value distribution). We try to check whether this feature is present in more realistic scenarios like Kuramoto Model perturbed by white noise and Kuramoto model on random networks. We verify that the Gumbel form of FPT is a universal feature irrespective of system size, coupling form, and coupling strength, with or without noise. We also found a parameter regime for minimum synchronisation time for the Kuramoto model with white noise.

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