1. Exploiting time scale differences : the quasi-steady-state-approximation
-- Michaelis Menten enzyme kinetics
-- Holling's functional response
-- excitable media: Fitzhugh-Nagumo
2. Phase plane analysis
Essentially an assignment : students work in couples through a series of exercises about prey-predator interaction. In a lecture we explain some key notions, such as linearized stability and Poincare-Bendixon.
3. Diffusion (mainly linear theory; partly in the form of assignments)
-- various derivations of the diffusion equation
-- the fundamental solution, superposition
-- transport by diffusion: what distance in how much time?
-- separation of variables, eigenfunctions/modes
-- the asymptotic speed of propagation
4. Reaction-Diffusion (nonlinearity)
-- travelling waves
-- scalar equations do NOT generate stable patterns (in convex domains)
-- Turing instability
-- bifurcation theory
-- transition layers (excitable systems)?
5. Age/size structured populations, cell cycle models
7. Branching processes, links to epidemiology (case study: antibiotic resistant bacteria in the ICU)
8. Adaptive Dynamics
and additional topics, as time permits.