title: Bifurcation study of phase oscillator systems with attractive and repulsive interaction.
abstract: We study a model of globally coupled phase oscillators that contains two groups of oscillators with positive (synchronizing) and negative (desynchronizing) incoming connections for the first and second groups, respectively. This model was previously studied by Hong and Strogatz (the Hong-Strogatz model) in the case of a large number of oscillators. We consider a generalized Hong-Strogatz model with a constant phase shift in coupling. Our approach is based on the study of invariant manifolds and bifurcation analysis of the system. In the case of zero phase shift, various invariant manifolds are analytically described and a new dynamical mode is found. In the case of a nonzero phase shift we obtained a set of bifurcation diagrams for various systems with three or four oscillators. It is shown that in these cases system dynamics can be complex enough and include multistability and chaotic oscillations.
authors.affiliation: Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkivska Strasse 3, 01601 Kyiv, Ukraine.
authors.forename: Oleksandr
authors.initials: O
authors.lastname: Burylko
authors.affiliation: Institute of Mathematical Problems of Biology, Russian Academy of Sciences, 142290 Pushchino, Russia.
authors.forename: Yakov
authors.initials: Y
authors.lastname: Kazanovich
authors.affiliation: Institute of Mathematical Problems of Biology, Russian Academy of Sciences, 142290 Pushchino, Russia and School of Computing and Mathematics, Plymouth University, Plymouth PL4 8AA, United Kingdom.
authors.forename: Roman
authors.initials: R
authors.lastname: Borisyuk
mesh_terms: D008962:Models, Theoretical; D010507:Periodicity