Resource Competition among Populations of Kuramoto Oscillators

The Kuramoto model has long been used to study the synchronization of populations of coupled oscillators. However, one shortcoming of the model as applied to physical systems is that true physical oscillations are not sustained indefinitely. Rather, sustained oscillations require energy. Further, the oscillators are often in competition for a limited supply of available energy. In prior work, we have extended the Kuramoto model by adding to it a resource dependence. In this work, we further allow for resource competition between the oscillators. The addition of competitive effects produces correlations between the synchronization states of different subpopulations of oscillators, for example allowing the synchronization state of one population of oscillators to be controlled only by varying the synchronization state of a distinct population, even when these two populations have no phase couplings between one another.