Asymmetric-interaction-induced dynamical states in globally coupled populations of conformists and contrarians

We consider two globally coupled populations of phase oscillators featuring as conformists and contrarians, respectively. By employing an asymmetric parameter for contrarians, we unravel the emergence of various collective dynamical states, including incoherent, chimera, phase clusters, quasiperiodic chimera, and frequency clusters states. Specifically, chimera, quasiperiodic chimera, and frequency clusters states emerge only for appropriate fractions of both conformists and contrarians, and for a large enough asymmetric parameter. We also show that the asymmetric parameter diminishes the spread of the bistable region and eventually leads to a second-order transition for larger coupling strengths of the contrarians. Further, the spread of the incoherent state decreases in the phase diagrams as the asymmetry between the contrarians is increased. Furthermore, libration of the collective phases onsets for the quasiperiodic chimera state and in the frequency clusters state. We deduce the evolution equations corresponding to the macroscopic order parameters using the finite-dimensional reduction by Watanabe and Strogatz. The analytical stability conditions obtained from the evolution equations for the macroscopic order parameters agree very well with the simulation boundaries of the dynamical states.