Self-organized spiral patterns at the edge of an order-disorder nonequilibrium phase transition

Italo'Ivo Lima Dias Pinto, Daniel Escaff, Alexandre Rosas

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We present a spatially extended version of the Wood-Van den Broeck-Kawai-Lindenberg stochastic phase-coupled oscillator model. Our model is embedded in two-dimensional (2d) array with a range-dependent interaction. The Wood-Van den Broeck-Kawai-Lindenberg model is known to present a phase transition from a disordered state to a globally oscillatory phase in which the majority of the units are in the same discrete phase. Here we address a parameter combination in which such global oscillations are not present. We explore the role of the interaction range from a nearest neighbor coupling in which a disordered phase is observed and the global coupling in which the population concentrate in a single phase. We find that for intermediate interaction range the system presents spiral wave patterns that are strongly influenced by the initial conditions and can spontaneously emerge from the stochastic nature of the model. Our results present a spatial oscillatory pattern not observed previously in the Wood-Van den Broeck-Kawai-Lindenberg model and are corroborated by a spatially extended mean-field calculation.

Original languageEnglish
Article number052215
JournalPhysical Review E
Issue number5
StatePublished - 1 May 2021

Bibliographical note

Funding Information:
The authors acknowledge Distinguished Professor Katja Lindenberg for valuable discussions and support throughout the development of this work. A.R. acknowledges Pronex/Fapesq-PB/CNPq Grant No. 151/2018 and CNPq Grant No. 308344/2018-9. D. E. acknowledges FONDECYT (Project No. 1211251). I.L.D.P. acknowledges the Army Research Laboratory. Research was sponsored by the Army Research Laboratory and was accomplished under Cooperative Agreement No. W911NFT20T2T0067. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Laboratory or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein.

Publisher Copyright:
© 2021 American Physical Society.


  • Initial conditions
  • Mean-field calculations
  • Nearest-neighbor coupling
  • Nonequilibrium phase transitions
  • Oscillatory patterns
  • Parameter combination
  • Phase-coupled oscillators
  • Two dimensional (2D) arrays


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