One step beyond linear stability analysis: the amplitude equation

Statistical Physics and Complexity Group meeting

One step beyond linear stability analysis: the amplitude equation

  • Event time: 11:30am
  • Event date: 16th February 2011
  • Speaker: Julien Tailleur (Formerly School of Physics & Astronomy, University of Edinburgh)
  • Location: Room 2511,

Event details

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.