MTH744

MTH744	Dynamical Systems
Lecturer: Thomas Prellberg	Semester 1, 2011/2012

News

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 description from the Maths UG Handbook
Module description from the Maths PG Handbook

Module information

Module syllabus
Module objectives
Last year's module webpage for MTH715U/MTHM021: Introduction to Dynamical Systems

Textbook

Nonlinear Dynamics and Chaos, Steven H. Strogatz, 1994

Lecture Notes

Lecture notes to be read in connection with the textbook.

Lecture and Exercise Class Plan (tentative!)

lecture	date	sections	content
1	29/9	1	Introduction
2	29/9	2.1	One-dimensional ODEs
	29/9		No Exercise class
3	6/10	2.2-2.3	Fixed Points and Stability
4	6/10	2.4-2.5	Linear Stability Analysis; Existence and Uniqueness
	6/10		Exercise class: 2.2.8,9; 2.3.1-4; 2.4.7,8
5	13/10	2.6-2.7	Impossibility of Oscillations; Potentials
6	13/10	3.1	Saddle-Node Bifurcations
	13/10		Exercise class: 2.7.7; 3.1.2,3,5
7	20/10	3.2	Transcritical Bifurcation
8	20/10	3.4	Pitchfork Bifurcation
	20/10		Exercise class: 3.2.4,6; 3.4.2,16
9	27/10	3.6	Imperfect Bifurcations
10	27/10	4.1-4.3	Flows on the circle
	27/10		Exercise class: 3.5.8; 3.6.2; 4.3.7
11	3/11	4.4	Flows on the circle
12	3/11	5.1	Two-dimensional linear flows
	3/11		Exercise class: 4.4.4; 5.1.2,9
			Reading Week: Insect Outbreak (3.7) and Fireflies (4.5)
13	17/11	5.2	Linear flows
14	17/11	6.1	Phase plane
	17/11		Exercise class: 5.1.12; 6.1.3,8
15	24/11	6.2-6.3	Phase plane (continued)
16	24/11	6.4	Lotka-Volterra model
	24/11		Exercise class: 6.2.2; 6.3.4,16
17	1/12	6.5-6.6	Conservative systems; Reversible Systems
18	1/12	7.1	Limit cycles
	1/12		Exercise class: 6.5.2; 6.6.3; 7.1.3
19	8/12	7.2	Ruling out closed orbits
20	8/12	7.3	Poincare-Bendixson Theorem
	8/12		Exercise class: 7.2.6,10; 7.3.1
21	15/12	9	The Lorenz equations and chaos
22	15/12	9	Chaos and strange attractors

Exam Paper

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

A sample exam paper together with solutions is available.

Thomas Prellberg
September 2011

MTH744

Dynamical Systems