MATH363-23S2 (C) Semester Two 2023

# Dynamical Systems

15 points

Details:
 Start Date: Monday, 17 July 2023 End Date: Sunday, 12 November 2023
Withdrawal Dates
Last Day to withdraw from this course:
• Without financial penalty (full fee refund): Sunday, 30 July 2023
• Without academic penalty (including no fee refund): Sunday, 1 October 2023

## Description

An introduction to nonlinear systems, the use of linearisation techniques and bifurcation theory.

Dynamical systems is the study of global, long-term behaviour of mathematical systems whose state evolves with time. Most of the systems studied arise from differential equations models of an applied problem from Physics, Biology, Economics, Chemistry, Engineering, etc. The aim of this course is to understand asymptotic behaviour using a combination of geometric reasoning, intelligent approximations, computer assistance and mathematical insight. This will be accomplished without grinding out the solutions of special classes of differential equations.

Topics covered: Overview of dynamics; flows on the line; one and two parameter bifurcations; 2d linear systems; phase plane for nonlinear 2d systems; limit cycles; Hopf bifurcations; applications; introduction to chaos in 3d flows.

## Learning Outcomes

• to develop insight into the qualitative behaviour of the solutions to differential equations; in particular, the effects of nonlinearity
• to obtain a greater understanding of the use of differential equations in modelling physical systems; including the role of parameters, and the interplay between solutions to the model and experiments
• to apply relevant computational and geometric techniques to analyse systems of differential equations; and to communicate the mathematical results clearly and coherently

## Prerequisites

MATH201 or EMTH210 and a further 15 points from (EMTH211, EMTH271, MATH202, MATH203, MATH240, MATH270).

## Assessment

Assessment Due Date Percentage
Tutorials 10%
Test 1 10 Aug 2023 10%
Test 2 28 Sep 2023 10%
Assign1 15%
Assign1 15%
Exam 40%

## Indicative Fees

Domestic fee \$824.00

International fee \$4,750.00

* All fees are inclusive of NZ GST or any equivalent overseas tax, and do not include any programme level discount or additional course-related expenses.

For further information see Mathematics and Statistics .

## All MATH363 Occurrences

• MATH363-23S2 (C) Semester Two 2023