The onset of vortex turbulence

The goal is to investigate some of the unusual and spectacular properties near the transition to turbulence in a two-dimensional field of limit-cycle oscillators. Of particular interest are the dynamics of topological defects (vortices) associated with the onset of turbulence. The complex Ginzburg-Landau equation describes an extended reaction-diffusion system close to the bifurcation of a steady state into a stable, periodic orbit. In the jargon of nonlinear dynamics, it is the amplitude equation corresponding to a Hopf bifurcation. Because of the generality of the assumptions under which it is derived, the complex Ginzburg-Landau equation describes systems in contexts other than chemical reactions with diffusion. Examples include Rayleigh-Benard convection and the phase fields of multimode lasers. The reaction-diffusion model is however, a sufficiently general model to frame our discussion.