Kardar-Parisi-Zhang fluctuations in the synchronization dynamics of limit-cycle oscillators

arxiv(2023)

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Abstract
The space-time process whereby one-dimensional systems of self-sustained oscillators synchronize is shown to display generic scale invariance, with scaling properties characteristic of the Kardar-Parisi-Zhang equation with columnar noise, and phase fluctuations that follow a Tracy-Widom probability distribution. This is revealed by a numerical exploration of rings of Stuart-Landau oscillators (the universal representation of an oscillating system close to a Hopf bifurcation) and rings of van der Pol oscillators, both of which are paradigms of self-sustained oscillators. The critical behavior is very well-defined for limit-cycle oscillations near the bifurcation point, and still dominates the behavior comparatively far from the bifurcation. In particular, the Tracy-Widom fluctuation distribution seems to be an extremely robust feature of the synchronization process. The nonequilibrium criticality here described appears to transcend the details of the coupled dynamical systems that synchronize, making plausible its experimental observation.
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