Quasiperiodic, periodic, and slowing-down states of coupled heteroclinic cycles

Dong Li*, M. C. Cross, Changsong ZHOU, Zhigang Zheng

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

9 Citations (Scopus)


We investigate two coupled oscillators, each of which shows an attracting heteroclinic cycle in the absence of coupling. The two heteroclinic cycles are nonidentical. Weak coupling can lead to the elimination of the slowing-down state that asymptotically approaches the heteroclinic cycle for a single cycle, giving rise to either quasiperiodic motion with separate frequencies from the two cycles or periodic motion in which the two cycles are synchronized. The synchronization transition, which occurs via a Hopf bifurcation, is not induced by the commensurability of the two cycle frequencies but rather by the disappearance of the weaker frequency oscillation. For even larger coupling the motion changes via a resonant heteroclinic bifurcation to a slowing-down state corresponding to a single attracting heteroclinic orbit. Coexistence of multiple attractors can be found for some parameter regions. These results are of interest in ecological, sociological, neuronal, and other dynamical systems, which have the structure of coupled heteroclinic cycles.

Original languageEnglish
Article number016215
JournalPhysical Review E
Issue number1
Publication statusPublished - 30 Jan 2012

Scopus Subject Areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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