Kardar-Parisi-Zhang universality class in the synchronization of oscillator lattices with time-dependent noise

Abstract

Systems of oscillators subject to time-dependent noise typically achieve synchronization for long times when their mutual coupling is sufficiently strong. The dynamical process whereby synchronization is reached can be thought of as a growth process in which an interface formed by the local phase field gradually roughens and eventually saturates. Such a process is here shown to display the generic scale invariance of the one-dimensional Kardar-Parisi-Zhang universality class, including a Tracy-Widom probability distribution for phase fluctuations around their mean. This is revealed by numerical explorations of a variety of oscillator systems: rings of generic phase oscillators and rings of paradigmatic limit-cycle oscillators, like Stuart-Landau and van der Pol. It also agrees with analytical expectations derived under conditions of strong mutual coupling. The nonequilibrium critical behavior that we find is robust and transcends the details of the oscillators considered. Hence, it may well be accessible to experimental ensembles of oscillators in the presence of e.g. thermal noise.

11 pages, 6 figures

References in corpus (12)

• Synchronization in complex networks
• Social physics
• Growing interfaces uncover universal fluctuations behind scale invariance
• Quantum gas microscopy of Kardar-Parisi-Zhang superdiffusion
• Observation of KPZ universal scaling in a one-dimensional polariton condensate
• Dynamics of magnetization at infinite temperature in a Heisenberg spin chain
• Random geometry and the Kardar-Parisi-Zhang universality class
• Kardar-Parisi-Zhang Physics in the Density Fluctuations of Localized Two-Dimensional Wave Packets
• Nonequilibrium criticality driven by Kardar-Parisi-Zhang fluctuations in the synchronization of oscillator lattices
• Kardar-Parisi-Zhang fluctuations in the synchronization dynamics of limit-cycle oscillators
• Phase-locking dynamics of heterogeneous oscillator arrays
• Synchronization and spacetime vortices in one-dimensional driven-dissipative condensates and coupled oscillator models

Cited by in corpus (6)

• Kardar-Parisi-Zhang scaling in time-crystalline matter
• Influence of coupling symmetries and noise on the critical dynamics of synchronizing oscillator lattices
• From Kardar-Parisi-Zhang scaling to soliton proliferation in Josephson junction arrays
• Nonconserved critical dynamics of the two-dimensional Ising model as a surface kinetic roughening process
• Scaling, Fractal Dynamics and Critical Exponents: Application in a non-integer dimensional Ising model
• Exponents and front fluctuations in the quenched Kardar-Parisi-Zhang universality class of one- and two- dimensional interfaces