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.
DOI
10.1103/physreve.90.022911
Publication Date
2014-08-25
Publication Title
Physical Review E
Volume
90
Issue
2
Publisher
American Physical Society (APS)
ISSN
1550-2376
Embargo Period
2024-11-22
Recommended Citation
Burylko, O., Kazanovich, Y., & Borisyuk, R. (2014) 'Bifurcation study of phase oscillator systems with attractive and repulsive interaction', Physical Review E, 90(2). American Physical Society (APS): Available at: https://doi.org/10.1103/physreve.90.022911
