Kardar-Parisi-Zhang fluctuations in the synchronization dynamics of limit-cycle oscillators
arXiv:2311.13253 · doi:10.1103/PhysRevResearch.6.033324
Abstract
The time-dependent process whereby one-dimensional systems of self-sustained oscillators synchronize is shown to display scale invariance in space and time, akin to that found in the dynamics of equilibrium critical phenomena. Remarkably, the process is largely independent of system details, sharing with a class of nonequilibrium surface kinetic roughening the universal scaling behavior of the Kardar-Parisi-Zhang equation with columnar noise, and featuring 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 paradigmatically supporting self-sustained oscillations. The critical behavior is very well defined for limit-cycle oscillations near bifurcation, and still dominates comparatively far from it. 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.
arXiv comment11 pages, 5 figures
References in corpus (26)
- Synchronization in complex networks
- Influence of Generic Scale Invariance on Classical and Quantum Phase Transitions
- Phase reduction approach to synchronization of nonlinear oscillators
- Generic Dynamic Scaling in Kinetic Roughening
- Quantum gas microscopy of Kardar-Parisi-Zhang superdiffusion
- A pedestrian's view on interacting particle systems, KPZ universality, and random matrices
- An appetizer to modern developments on the Kardar-Parisi-Zhang universality class
- Super-roughening versus intrinsic anomalous scaling of surfaces
- Phase Diagram of the Two-Dimensional Complex Ginzburg-Landau Equation
- Observation of KPZ universal scaling in a one-dimensional polariton condensate
- Surprising mappings of 2D polar active fluids to 2D soap and 1D sandblasting
- Family-Vicsek Scaling of Roughness Growth in a Strongly Interacting Bose Gas
- Clustering in Globally Coupled Oscillators Near a Hopf Bifurcation: Theory and Experiments
- From Kardar-Parisi-Zhang scaling to explosive desynchronization in arrays of limit-cycle oscillators
- Impact of Dissipation on Universal Fluctuation Dynamics in Open Quantum Systems
- Dynamical Scaling of Surface Roughness and Entanglement Entropy in Disordered Fermion Models
- Synchronization in disordered oscillatory media: a nonequilibrium phase transition for driven-dissipative bosons
- Characteristic Lyapunov vectors in chaotic time-delayed systems
- Kardar-Parisi-Zhang Physics in the Density Fluctuations of Localized Two-Dimensional Wave Packets
- Kardar-Parisi-Zhang universality class for the critical dynamics of reaction-diffusion fronts
- Nonequilibrium criticality driven by Kardar-Parisi-Zhang fluctuations in the synchronization of oscillator lattices
- Roughening of the anharmonic Larkin model
- Universal dynamic scaling in chemical reactions at and away from equilibrium
- Random Matrix Ensembles in Hyperchaotic Classical Dissipative Dynamical Systems
- Phase-locking dynamics of heterogeneous oscillator arrays
- Initial perturbation matters: implications of geometry-dependent universal Kardar-Parisi-Zhang statistics for spatiotemporal chaos
Cited by in corpus (6)
- Kardar-Parisi-Zhang universality class in the synchronization of oscillator lattices with time-dependent noise
- 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
- Exponents and front fluctuations in the quenched Kardar-Parisi-Zhang universality class of one- and two- dimensional interfaces