Chimera and modulated drift states in a ring of nonlocally coupled oscillators with heterogeneous phase lags

We consider a ring of phase oscillators with nonlocal coupling strength and heterogeneous phase lags. We analyze the effects of heterogeneity in the phase lags on the existence and stability of a variety of steady states. A nonlocal coupling with heterogeneous phase lags that allows the system to be solved analytically is suggested and the stability of solutions along the Ott-Antonsen invariant manifold is explored. We present a complete bifurcation diagram for stationary patterns including the uniform drift and modulated drift states as well as chimera state, which reveals that the stable modulated drift state and a continuum of metastable drift states could occur due to the heterogeneity of the phase lags. We verify our theoretical results using the direct numerical simulations of the model system.