Stochastic population models, spring 2017

Teacher: Stefan Geritz 

Scope: 10 cr

Type: Advanced studies

Teaching:

This is a course about population models that cannot be properly described or analysed in a purely deterministic way because of the presence of noise. We consider two kinds of noise depending on its origin: The noise may be exogenous, i.e., due to autonomous processes external to the population itself and affecting it by causing population parameters to fluctuate in time. The noise may also be endogenous, i.e., due to stochastic demographic in the number of births and deaths within any given interval of time.

Topics:

Basic notions in model formulation and analysis: the principle of mass-action; growth and development; equilibria and local stability; elements of the theory of Poincare and Bendixon.

The population as a filter of externally generated noise: ordinary differential equations and delay-differential equations; impulse response; frequency response; transfer function; filter characteristics of the population model.

The population as the source of noise: single-type and multi-type birth-death processes; demographic noise; stochastic processes and ergodicity; the Fokker-Planck equation; stochastic differential equations; autocorrelation function and spectral density.

Prerequisites:

Ordinary differential equations; elements of real and complex analysis