The dynamics of chimera states in heterogeneous Kuramoto networks

We study a variety of mixed synchronous/incoherent (“chimera”) states in several heterogeneous networks of coupled phase oscillators. For each network, the recently-discovered Ott–Antonsen ansatz is used to reduce the number of variables in the partial differential equation (PDE) governing the evolution of the probability density function by one, resulting in a time-evolution PDE for a variable with as many spatial dimensions as the network. Bifurcation analysis is performed on the steady states of these PDEs. The results emphasise the commonality of the dynamics of the different networks, and provide stability information that was previously inferred.