Exploring synchronized oscillations in Kuramoto-type oscillators with nonlinear feedback

Synchronization is a hallmark of complex systems, emerging from the interplay of randomness, coupling and nonlinear dynamics. In this project, we explore synchronization in a system of coupled oscillators using the Kuramoto model, with an additional nonlinear feedback term. We examine how frequency distributions, coupling strength and network topology influence synchronization. We study the time series of the phases of the oscillators for fully-connected and loosely-connected networks, and also for different lattices (toroidal, square and hexagonal). We also investigate cluster synchronization arising from multimodal frequency distributions. Together, these results show how randomness (in the initial phases and frequencies of the oscillators), combined with coupling and nonlinear feedback, gives rise to rich collective behavior.