Wednesday 16 Feb 11 - 11:30am
One step beyond linear stability analysis: the amplitude equation
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.