Finite-dimensional models of the Ginzburg-Landau equation

In this paper we study truncated finite dimensional models of theinfinite-dimensional equation describing the evolution of even, space-periodic solutionsofthe Ginzburg-Landau equation. We derive estimates on the position of the globalattractor of the flow, which yield that the magnitude of the Mth mode of the globalattractor decays faster than any algebraic power of M-'. The estimates are independentof the dimension of the model. In a numerical section we simulate the Row for threeradical low-dimensional models (of two, three and four complex modes); we analyse theinhence oi ihe number oi modes on the giabai dynamics. Tie iour-dimensionai modeiexhibits the same intricate flow-characteristics as the 32-dimensional model studied byKeefe.