Turbulence and Linear Stability in a Discrete Ginzburg-Landau Model
The Complex Ginzburg-Landau partial differential equation appears in many interesting none-quilibrium dynamical systems. It describes an extended system close to a global Hopf bifurcation  such as occurs e.g. in oscillatory chemical reactions like the Belousov-Zhabotinsky reaction . In two recent papers [3–4] we have discussed a discrete, “map lattice” version of this equation, analysed the dynamics of vortices and the onset of turbulence. The main results were that vortices can get bound together in “entangled” states where their cores do not move and that the system has a well-defined transition to turbulence below the linear instability threshold for the uniform state. It remains to be seen which of our results will be valid for the continuum Ginzburg-Landau equation; but recently an analytic treatment of the motion of a pair of vortices leads to bound states analogously to our entangled states .
KeywordsHopf Bifurcation Linear Stability Uniform State Plane Wave Solution Oscillatory Chemical Reaction
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