Dynamical Systems

This a lecture course in Part II of the Mathematical Tripos (for third-year undergraduates). The notes are a small perturbation to those presented in previous years by Mike Proctor. I gave this course in the academic years 2012-2015. I leave the lecture notes here in case they are helpful, but Cambridge undergraduates taking this course are very trongly advised to attend the current lectures and may find the notes for those much better than mine.

Lecture Notes PDF File

Lecture Notes with diagrams PDF File. These were not intended for distribution -- the diagrams are crudely hand-drawn -- but several people have given reasons why they need the diagrams, so here they are.

Example Sheet 1 PDF File

Example Sheet 2 PDF File

Example Sheet 3 PDF File

Example Sheet 4 PDF File

Matlab program: solves system considered in Example 20. Specify parameter 'a'. Specify initial condition using mouse.

Matlab program: solves system considered in Examples 26 and 27. Plots contours of H(x,y) for the unperturbed system with 'epsilon'=0. Specify parameters 'epsilon' and 'a'. Specify initial condition using mouse.

Matlab program: solves Van der Pol equation. Specify parameter 'beta'. Plots nullclines. Specify initial condition using mouse.