Hopf bifurcation and multistability in a system of phase oscillators

Sergey Astakhov*, Naoya Fujiwara, Artem Gulay, Naofumi Tsukamoto, Juergen Kurths

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


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 2 pi-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.

Original languageEnglish
Article number032908
Number of pages8
JournalPhysical Review. E, Statistical, Nonlinear and Soft Matter Physics
Issue number3
Publication statusPublished - 11 Sept 2013


  • chaotic oscillators
  • synchronization
  • entrainment
  • networks
  • dynamics


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