Journal
JOURNAL OF NONLINEAR SCIENCE
Volume 20, Issue 1, Pages 105-129Publisher
SPRINGER
DOI: 10.1007/s00332-009-9053-2
Keywords
Synchronization; Coupled oscillators; Heteroclinic ratchet; Asymmetric desynchronization; Synchrony-breaking bifurcation
Categories
Ask authors/readers for more resources
We analyze an example system of four coupled phase oscillators and discover a novel phenomenon that we call a heteroclinic ratchet; a particular type of robust heteroclinic network on a torus where connections wind in only one direction. The coupling structure has only one symmetry, but there are a number of invariant subspaces and degenerate bifurcations forced by the coupling structure, and we investigate these. We show that the system can have a robust attracting heteroclinic network that responds to a specific detuning Delta between certain pairs of oscillators by a breaking of phase locking for arbitrary Delta > 0 but not for Delta a parts per thousand currency sign0. Similarly, arbitrary small noise results in asymmetric desynchronization of certain pairs of oscillators, where particular oscillators have always larger frequency after the loss of synchronization. We call this heteroclinic network a heteroclinic ratchet because of its resemblance to a mechanical ratchet in terms of its dynamical consequences. We show that the existence of heteroclinic ratchets does not depend on symmetry or number of oscillators but depends on the specific connection structure of the coupled system.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available