Özkan Karabacak
580 California St., Suite 400
San Francisco, CA, 94104
Heteroclinic Ratchets in Networks of Coupled Oscillators
2009, Journal of Nonlinear Science
https://doi.org/10.1007/S00332-009-9053-2
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Abstract
We study an unusual but robust phenomenon that appears in an example system of four coupled phase oscillators. The coupling is preserved under 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 attractor that responds to a specific detuning ∆ between certain pairs of the oscillators by a breaking of phase locking for arbitrary ∆ > 0 but not for ∆ ≤ 0. As the dynamical mechanism behind this is a particular type of heteroclinic network, we call this a 'heteroclinic ratchet' because of its dynamical resemblance to a mechanical ratchet.
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