Chimeras in phase oscillator networks locally coupled through an auxiliary field: Stability and bifurcations

We study networks in the form of a lattice of nodes with a large number of phase oscillators and an auxiliary variable at each node. The only interactions between nodes are nearest-neighbor. The Ott/Antonsen ansatz is used to derive equations for the order parameters of the phase oscillators at each node, resulting in a set of coupled ordinary differential equations. Chimeras are steady states of these equations, and we follow them as parameters are varied, determining their stability and bifurcations. In two-dimensional domains, we find that spiral wave chimeras and rotating waves have significantly different properties than those in networks with nonlocal coupling.