title: Hopf bifurcation and multistability in a system of phase oscillators.
abstract: We study the phase reduction of two coupled van der Pol oscillators with asymmetric repulsive coupling under an external harmonic force. We show that the system of two phase oscillators undergoes a Hopf bifurcation and possesses multistability on a 2π-periodic phase plane. We describe the bifurcation mechanisms of formation of multistability in the phase-reduced system and show that the Andronov-Hopf bifurcation in the phase-reduced system is not an artifact of the reduction approach but, indeed, has its prototype in the nonreduced system. The bifurcational mechanisms presented in the paper enable one to describe synchronization effects in a wide class of interacting systems with repulsive coupling e.g., genetic oscillators.
authors.affiliation: Physics Department, Chair of Radiophysics and Nonlinear Dynamics, Saratov State University, 410012 Saratov, Russia.
authors.forename: Sergey
authors.initials: S
authors.lastname: Astakhov
authors.forename: Naoya
authors.initials: N
authors.lastname: Fujiwara
authors.forename: Artem
authors.initials: A
authors.lastname: Gulay
authors.forename: Naofumi
authors.initials: N
authors.lastname: Tsukamoto
authors.forename: Jürgen
authors.initials: J
authors.lastname: Kurths