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A system of four coupled oscillators that exhibits unusual synchronizationphenomena has been ana- lyzed. Existence of a one-way heteroclinic network,called heteroclinic ratchet, gives rise to uni-directional (de)synchronizationbetween certain groups of cells. Moreover, we show that locking in frequencydiffer- ences occur when a small white noise is added to the dynamics ofoscillators.

Uni-directional synchronization and frequency difference locking induced by a heteroclinic ratchet