Synchronization of coupled second-order Kuramoto oscillators

Synchronization is a ubiquitous phenomenon in nature and engineering. In this project, we explore the effect of the oscillators’ inertia on their synchronization. To do that, we develop a unified framework based on the self-consistent approach to describe the synchronization processes in systems ranging from infinite to finite networks of oscillators, from having one to several synchronized clusters, and from a single parameter to several interacting parameters. We comprehensively study how the microscopic oscillator dynamics is related to the macroscopic synchronization processes, and the cross-effect of inertias with other parameters. Through our approach we can explain why synchronization processes are continuous, or abrupt with hysteresis, or exhibit a cascading formation of several synchronized clusters. Finally, using our results we can tune the parameters to control the type of synchronization processes, such as continuous, abrupt, or even a mixture of these two behaviors.