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On the relation between Vicsek and Kuramoto models of spontaneous synchronization

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  • Chepizhko, A.A.
  • Kulinskii, V.L.

Abstract

The Vicsek model for self-propelling particles in 2D is investigated with respect to the addition of the stochastic perturbation of dynamic equations. We show that this model represents in essence the same type of bifurcations under a different type of noise as the celebrated Kuramoto model of spontaneous synchronization. These models demonstrate similar behavior at least within the mean-field approach. To prove this we consider two types of noise for the Vicsek model which are commonly considered in the literature: the intrinsic and the extrinsic ones (according to the terminology of Pimentel et al. [J.A. Pimentel, M. Aldana, C. Huepe, H. Larralde, Intrinsic and extrinsic noise effects on phase transitions of network models with applications to swarming systems, Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 77 (6) (2008) doi:10.1103/PhysRevE.77.061138. URL: http://dx.doi.org/10.1103/PhysRevE.77.061138]). The qualitative correspondence with the bifurcation of stationary states in the Kuramoto model is stated. A new type of stochastic perturbation—the “mixed” noise is proposed. It is constructed as the weighted superposition of the intrinsic and the extrinsic noises. The corresponding phase diagram “noise amplitude vs. interaction strength” is obtained. The possibility of the tricritical behavior for the Vicsek model is predicted.

Suggested Citation

  • Chepizhko, A.A. & Kulinskii, V.L., 2010. "On the relation between Vicsek and Kuramoto models of spontaneous synchronization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(23), pages 5347-5352.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:23:p:5347-5352
    DOI: 10.1016/j.physa.2010.08.016
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    References listed on IDEAS

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    1. Ratushnaya, V.I. & Bedeaux, D. & Kulinskii, V.L. & Zvelindovsky, A.V., 2007. "Collective behavior of self-propelling particles with kinematic constraints: The relation between the discrete and the continuous description," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 381(C), pages 39-46.
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    Cited by:

    1. Chepizhko, Oleksandr & Kulinskii, Vladimir, 2014. "The hydrodynamic description for the system of self-propelled particles: Ideal Viscek fluid," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 415(C), pages 493-502.

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