Spring

Unit(s) of Assessment	Weighting Towards Module Mark( %)
Coursework: In the form of a test and an assignment which will involve the use of Maple.	25
Exam: Written examination (2 hours, unseen).	75
Qualifying Condition(s)              A weighted aggregate mark of 40% is required to pass the module.

None.

Introduce the main features of nonlinear dynamical systems (with applications) and techniques for analysing such systems.

At the end of the course, students should be able to
• Analyse simple bifurcations in nonlinear dynamical systems
• Analyse the common routes to chaos in dynamical systems, and
• Analyse simple chaotic iterated maps.

The course covers the following topics:
• Topological dynamics of ordinary differential equations
• Saddle-node, transcritical, pitchfork, Hopf, period-doubling and homoclinic bifurcations of ordinary differential equations
• One-dimensional iterated maps, bifurcations and topological conjugacy
• Period-doubling route to chaos, universality and renormalisation in 1D iterated maps
• Lyapunov exponents and sensitive dependence on initial conditions of 1D iterated maps
• Chaotic 1D maps (Doubling and tent maps) and symbolic dynamics
• Fractal geometry and non-integer dimension
• Strange attractors and repellers
• Applications: population dynamics, classical mechanics, chemical oscillations etc.

Teaching is by lectures and tutorials. Learning takes place through lectures, tutorials, exercises, coursework and background reading. 3 lecture/tutorial hours per week for 10 weeks.

Further Reading
Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering, Steven H. Strogatz, Westview, 2000.
Does God play Dice?, Ian Stewart, Oxford Press, 1989.
Mathematical Biology: Part I, J. D. Murray, Springer-Verlag, 2002.

14 September 2009