Competition and Bifurcations in Phase Oscillator Networks with Positive and Negative Couplings

We consider Kuramoto-Sakaguchi type model of globally coupled phase oscillators with positive and negative coupling parameters. Such type of model with natural motivation was proposed for consideration by H. Hong and S.H. Strogatz where they obtained interesting and unexpected results. Our aim is to do bifurcation analysis for the finite-dimensional case of identical oscillators when phase shift is involved. We describe invariant manifolds and find complicated heteroclinic constructions, chaos and multistability in the system.