Note: This module may not be running next year (2012/13) so 2nd years are advised not to plan to take it as 3rd years.
Content: This module is designed to be a gentle introduction to the area of non-linear dynamical systems by way of its application to the "Natural World''. Some quite deep ideas are introduced to help explain or describe natural phenomena such as evolutionary theory, species diversity, weather forecasting, animal locomotion and epidemics. The mathematics considered will cover the full spectrum of nonlinear dynamical systems theory including game theory, nonlinear oscillations, symmetry, sensitive dependence upon initial conditions (chaos) and (if time permits) fractals. In many cases these ideas are introduced outside of a rigorous setting so that the beauty and power of the techniques can be explored. There will be occasional reference to numerical solutions of some problems, and some of the assessed work may require use of a computer, but no previous experience (or love) of computing will be assumed.
Aims: To provide a general introduction to the many aspects of dynamical systems theory through its application to the "Natural World''.
Objectives: At the end of the module you should be familiar with the ideas of stable/unstable equilibria and periodic orbits, strange attractors, Poincaré maps, bifurcations, catastrophes, nonlinear oscillations, chaos and fractals.
There is no one textbook which adequately covers the whole module, but J.D. Murray Mathematical Biology or it's recent revision Mathematical Biology I: An Introduction is recommended for many aspects. Other suggestions will be made during the course.