Science and Engineering at The University of Edinburgh

Theory Club

Wednesday 16 Feb 11 - 11:30am

One step beyond linear stability analysis: the amplitude equation

Julien Tailleur

When studying non-linear dynamical systems, the recipe is often the same: find the equilibria, linearize the equations around them, Fourier transform the equations and compute the growth rate of the perturbations as a function of their wave-length. That's a great recipe to find a transition beyond which a system becomes unstable. What is less known is that in many cases, it is possible to compute the amplitude of the perturbations and not just its wave-length. That's the purpose of the amplitude equation, which I will present and illustrate.

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