Synchronization of Globally Coupled Nonlinear Oscillators: the Rich Behavior of the Kuramoto Model

Global synchronization of oscillators is found abundantly in nature, emerging in fields from physics to biology. The Kuramoto model describes the synchronization behavior of a generalized system of interacting oscillators. With a large number of oscillators with different natural frequencies, the Kuramoto model predicts that, if they are allowed to interact strongly enough, they will all start oscillating at the same rate. The model provides a mathematical basis for studying the conditions under which synchronization can occur. For example, it is possible to solve for the critical amount of coupling needed among the oscillators to have synchronization. My research involved studying the basics of Kuramoto’s analysis and then investigating how the synchronization behavior is affected by random noise. Numerical simulations were run with and without noise to supplement and verify the analytical results.