Frozen dynamics and synchronization through a secondary symmetry-breaking bifurcation

Abstract

We show evidence of the frozen dynamics (Kibble-Zurek mechanism) at the transition one-dimensional (1D) front of an extended 1D array of convective oscillators that undergo a secondary subcritical bifurcation. Results correspond to a global synchronization process from nonlocal coupling between the oscillating units. The quenched dynamics exhibits defect trapping at the synchronization front according to the Kibble-Zurek mechanism, predicted for condensed matter systems. A stronger subcriticality prevents the fronts from freezing defects during the quenched transitions. A synchronization model of supercritical oscillating units is proposed to explain differentiation mechanisms in morphogenesis above a critical crossing rate when the frequency of the individual oscillators becomes coherent. The phases of such oscillators are spatially coupled through a Kuramoto-Battogtokh term that leads to the experimentally observed subcriticality. As a consequence, we show that the Kibble-Zurek mechanism overcomes non-locality of a geometrical network above a critical crossing rate. © 2013 American Physical Society.