The Complex Ginzburg Landau equation (CGLe) Mostly a Tutorial 1.Introduction 2.0D: The Hopf bifurcation (textbooks!) 3.Spatially extended systems, predominantly.

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Presentation transcript:

The Complex Ginzburg Landau equation (CGLe) Mostly a Tutorial 1.Introduction 2.0D: The Hopf bifurcation (textbooks!) 3.Spatially extended systems, predominantly (standard!) 4.General discussion: wave number band (phase waves) etc. 5.Solutions in 1D: coherent structures (localised states, fronts, Retracting Fronts, phase chaos and defect chaos…) 6. Solutions in 2D (and maybe 3D) vortices and spirals, chaos… What would Landau have said? Pathological ?

The Hopf Bifurcation. Poincare considered the problem too trivial to write down…. Andronov & Leontovich did it in the plane ( ~1938). Hopf generalized it to many dergrees of freedom (1942). u v u v In the plane: Ha-ha-ha!

Re (A)u Actually a structure for Snapshot!