Courses & Units

Dynamical Systems and Chaos KYA314

Introduction

This is a physics and mathematics discipline elective unit. Recommended for students doing an Honours in Physics or Applied Mathematics. Suitable unit for graduate students in interdisciplinary applied science who lack theoretical background in dynamical systems. Offered only in odd years. Teaching arrangements include weekly lectorials, workshops, and independent study computer lab sessions. On completion of this course, students will be able to apply theoretical concepts to the analysis of real-world systems. Topics covered include: Linear and Non-linear systems, examples. Phase plane and phase space. The Hartmann Linearization Theorem. Co-dimension 1 bifurcations; saddle-node, pitchfork and Hopf bifurcations. Limit cycles and oscillations. Global bifurcations. Homoclinic and heteroclinic orbits. Characterization of chaos. Routes to chaos, period doubling, secondary Hopf bifurcations, intermittency. Homoclinic chaos. Mel'nikov theory. Students will also learn basic numerical recipes for analysing complex dynamical systems and their applications.

Summary

Unit name Dynamical Systems and Chaos
Unit code KYA314
Credit points 12.5
College/School College of Sciences and Engineering
School of Natural Sciences
Discipline Physics
Coordinator Doctor Courtney Quinn
Available as an elective? Yes
Delivered By University of Tasmania
Level Advanced

Availability

This unit is currently unavailable.

Note

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* The Final WW Date is the final date from which you can withdraw from the unit without academic penalty, however you will still incur a financial liability (refer to How do I withdraw from a unit? for more information).

Unit census dates currently displaying for 2024 are indicative and subject to change. Finalised census dates for 2024 will be available from the 1st October 2023. Note census date cutoff is 11.59pm AEST (AEDT during October to March).

About Census Dates

Learning Outcomes

  • Explain the ways in which dynamical systems exhibiting chaos can arise in the fields of mathematics, physics, engineering and other domains.
  • Use/apply mathematical concepts and techniques to analyse of the behaviour of dynamical systems.
  • Apply a wide range of mathematical and computational techniques to determine the local and global behaviour of dynamical systems by understanding bifurcations and equilibrium points.
  • Interpret and present information communicated in mathematical and plain English form.
  • Demonstrate personal and social responsibility in the ethical application of approaches to problem solving, self-directed learning, and group learning.

Fee Information

The 2024 Commonwealth Supported Place (CSP) rates are still being finalised by the Government and we will update the domestic fee information as soon as we have more details.

Requisites

Prerequisites

Admission into a relevant Masters course OR (KMA252 and KMA254) OR (KYA211 and KYA212) OR (KYA375 - Engineering Physics AND KME271 - Engineering Mathematics)

Teaching

Teaching Pattern

3 x 50 minute lectorials weekly, 1 x 50 minute workshop weekly, 1 x 2 hour optional computer lab drop-in session weekly

AssessmentOral exam (10%)|Project (20%)|Assignments (30%)|Examination (40%)
TimetableView the lecture timetable | View the full unit timetable

Textbooks

Required

Required readings will be listed in the unit outline prior to the start of classes.
LinksBooktopia textbook finder

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