Dynamical Systems

Lecturer: Thomas Prellberg Semester 1, 2011/2012

News
• Jun 5: The 2012 exam paper is now available
• Apr 23: Revision lecture April 27, 11-12, Queens EB4. Exam May 24, 10-1
• Jan 19: A sample exam paper is now available
• Dec 15: Lecture notes are now complete
• Oct 13: Tue office hours moved to 1:30-2:30, Thu office hours moved to Fri 10:30-11:30
• Sep 24: updated module description, syllabus, and learning outcomes

Lecture times
• Thu 11-12 and 12-1, Maths room 203, starting on September 29
Exercise classes
• Thu 3-4, Maths rooom 203, starting on October 6
Office hours
• Normally Tue 1:30-2:30, Fri 10:30-11:30 in Maths B51. Please check here for up-to-date information
Module description

A dynamical system is any system which evolves over time according to some pre-determined rule. The goal of dynamical systems theory is to understand this evolution. This module develops the theory of dynamical systems systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations and chaos. Much emphasis is placed on applications.

Module information

Textbook

Lecture Notes
Lecture and Exercise Class Plan (tentative!)

lecturedatesectionscontent
129/91Introduction
229/92.1One-dimensional ODEs
29/9No Exercise class
36/102.2-2.3Fixed Points and Stability
46/102.4-2.5Linear Stability Analysis; Existence and Uniqueness
6/10Exercise class: 2.2.8,9; 2.3.1-4; 2.4.7,8
513/102.6-2.7Impossibility of Oscillations; Potentials
13/10Exercise class: 2.7.7; 3.1.2,3,5
720/103.2Transcritical Bifurcation
820/103.4Pitchfork Bifurcation
20/10Exercise class: 3.2.4,6; 3.4.2,16
927/103.6Imperfect Bifurcations
1027/104.1-4.3Flows on the circle
27/10Exercise class: 3.5.8; 3.6.2; 4.3.7
113/114.4Flows on the circle
123/115.1Two-dimensional linear flows
3/11Exercise class: 4.4.4; 5.1.2,9
Reading Week: Insect Outbreak (3.7) and Fireflies (4.5)
1317/115.2Linear flows
1417/116.1Phase plane
17/11Exercise class: 5.1.12; 6.1.3,8
1524/116.2-6.3Phase plane (continued)
1624/116.4Lotka-Volterra model
24/11Exercise class: 6.2.2; 6.3.4,16
171/126.5-6.6Conservative systems; Reversible Systems
181/127.1Limit cycles
1/12Exercise class: 6.5.2; 6.6.3; 7.1.3
198/127.2Ruling out closed orbits
208/127.3Poincare-Bendixson Theorem
8/12Exercise class: 7.2.6,10; 7.3.1
2115/129The Lorenz equations and chaos
2215/129Chaos and strange attractors

Exam Paper

Revision lecture April 27, 11-12, Queens EB4. Exam May 24, 10-1.

Thomas Prellberg
September 2011