Hole Structures in Nonlocally Coupled Noisy Phase Oscillators

TL;DR

This paper shows that nonlocally coupled noisy phase oscillators can form hole structures in their spatial phase distribution, modeled by a nonlinear Fokker-Planck equation and related to the Nozaki-Bekki solution of the complex Ginzburg-Landau equation.

Contribution

It demonstrates the emergence of hole structures in a system of noisy phase oscillators and connects these phenomena to known solutions of the complex Ginzburg-Landau equation.

Findings

Hole structures appear in the spatial phase distribution.

The phase model reduces to the complex Ginzburg-Landau equation near bifurcation.

Numerical simulations confirm the presence of hole structures.

Abstract

We demonstrate that a system of nonlocally coupled noisy phase oscillators can collectively exhibit a hole structure, which manifests itself in the spatial phase distribution of the oscillators. The phase model is described by a nonlinear Fokker-Planck equation, which can be reduced to the complex Ginzburg-Landau equation near the Hopf bifurcation point of the uniform solution. By numerical simulations, we show that the hole structure clearly appears in the space-dependent order parameter, which corresponds to the Nozaki-Bekki hole solution of the complex Ginzburg-Landau equation.