Analysis on Patterns of Globally Coupled Phase Oscillators with Attractive and Repulsive Interactions

The Hong-Strogatz(HS) model of globally coupled phase oscillators with attractive and repulsive interactions reflects the fact that each individual(oscillator) has its own attitude(attractive or repulsive) to the same environment(mean Seld).Previous studies on HS model focused mainly on the stable states on Ott-Antonsen(OA)manifold.In this paper,the eigenvalues of the Jacobi matrix of each fixed point in HS model are explicitly derived,with the aim to understand the local dynamics around each fixed point.Phase transitions are described according to reJative population and coupling strength.Besides,the dynamics off OA manifold is studied.