Homepage for Bifurcations and Chaos 2014

This course is concerned with the application of methods from dynamical systems and bifurcation theories to the study of nonlinear oscillations. The mathematical models we consider are (fairly small) sets of ordinary differential equations and mappings. As examples we look at nonlinear oscillations: the famous oscillators of van der Pol and Duffing, the Lorenz equations, and a bouncing ball problem. We show that the solutions of these problems can be markedly chaotic and that they seem to possess strange attractors: attracting motions which are neither periodic nor quasiperiodic. In order to develop the idea of chaos, we discuss the Smale horseshoe map and describe the method of symbolic dynamics. Moreover, we analyse global homoclinic and heteroclinic bifurcations and illustrate the results with the examples of the nonlinear oscillators.
Literature:  Nonlinear oscillations, dynamical systems, and bifurcations of vector fields. Applied Mathematical Sciences, J. Guckenheimer, P. Holmes, Vol. 42, Springer-Verlag, New York, 1983, ISBN 0-3879-0819-6
Instructor: Vivi Rottschäfer
Office: 206

Assistent: Corine Meerman
Email: cmeerman[at]math.leidenuniv.nl
Office: 204

Assignment Set 1
Deadline: 17 March 2014, 17:00

Assignment Set 2
Deadline: 7 April 2014, 17:00

Assignment Set 3
Deadline: 12 May 2014, 17:00

The deadlines for the assignments are strict!

Lecture schedule:

6 Feb
2.2, 1.5 (Poincare map intermezzo)
13 Feb 2.2 (cont.), 4.1
20 Feb 4.1 (cont.), 4.2
27 Feb 4.3, 4.5
6 March

13 March no class
20 March
27 March
3 April

10 April
17 April no class
24 April ? no class
1 May
8 May

15 May
21 May