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 6. Chemotaxis 7. Branching processes, links to epidemiology (case study: antibiotic resistant bacteria in the ICU) 8. Adaptive Dynamics and additional topics, as time permits. |