Chimeras in the two-community Kuramoto model with an external drive

Abstract

We study the bifurcations of a special case of the Kuramoto model with two communities of oscillators and an external drive. We use Ott-Antonsens ansatz to derive the low-dimensional system of differential equations that governs the macroscopic dynamics of the high-dimensional problem. The choice of parameters of the system is motivated by the search for so-called Chimera states; stable phase configurations with partial synchronization. Our main result is the derivation of the low-dimensional system following Ott-Antonsens Ansatz and findings of periodic and chaotic Chimeras.