Bifurcations and complex dynamics

First, bifurcation theory and asymptotic methods will be presented and applied to a variety of
problems such as cloud convection, long time evolution of population dynamics, tipping points
in climate dynamics. Second, in many situations of interest in nature, fluid flows are turbulent.
The effects of turbulent fluctuations on bifurcating systems will thus be presented. We will for
instance discuss how periodic modulation over a fluctuating background can trigger stochastic
resonance in a climatic system, or how the generation of magnetic energy in a dynamo is
affected by turbulence.
Additional topics include feedback-driven instabilities, oscillator networks, and the emergence
of chaotic behavior in driven nonlinear systems.