Ordinary differential equations and dynamical systems (MATH3101)

Course overview

Prior to 2022, this course was titled: Bifurcation and Chaos. Local theory of ODEs; n-dimensional linear systems of ODEs and normal forms; stability and bifurcation theory; one-dimensional maps; introduction to chaos.

This is a course on the qualitative methods for nonlinear ordinary differential equations and dynamical systems.

Starting with the idea of Phase Space, we will investigate the existence of solutions, stability and bifurcations of stationary points and periodic orbits. This is followed by a discussion of the stationary points of maps and their bifurcations which leads naturally to a discussion of chaos in one dimensional maps. Finally we investigate chaos in continuous systems such as the Lorenz system.

In the School of Mathematics and Physics we are committed to creating an inclusive and empowering learning environment for all students. We value and respect the diverse range of experiences our students bring to their education, and we believe that this diversity is crucial for fostering a rich culture of knowledge sharing and meaningful exploration. We hold both students and staff accountable for actively contributing to the establishment of a respectful and supportive learning environment.

Bullying, harassment, and discrimination in any form are strictly against our principles and against ﾠUQ Policy,ﾠ and will not be tolerated. We have developed a ﾠsuite of resourcesﾠ to assist you in recognising, reporting, and addressing such behaviour. If you have any concerns about your experience in this course, we encourage you to tell a member of the course teaching team, or alternatively contact an SMP Classroom Inclusivity Champion (see Blackboard for contact details). Our Inclusivity Champions are here to listen, to understand your concerns, and to explore potential actions that can be taken to resolve them. Your well-being and a positive learning atmosphere are of utmost importance to us. ﾠﾠ

Course requirements

Assumed background

Some previous knowledge of ODEs is assumed. In particular solving linear constant coeffcient ODEs and nonlinear first order ODEs via the method of separation of variables. Students should also be familiar with linear systems of ODEs, fundamental matrices and phase plane analysis for linear 2D systems with constant coefficients, although this last topic is reviewed.

Prerequisites

You'll need to complete the following courses before enrolling in this one:

(MATH2400 or MATH2401) + (MATH2001 or MATH2901) + (MATH2010 or MATH2100)

Jointly taught details

This course is jointly-taught with:

MATH3101 and MATH7131 are co-badged courses and will share learning activities. MATH7131 will have some differences in assessment to evaluate students at Level 9 (Masters) of the Australian Qualifications Framework.

Course contact

Course staff

Timetable

The timetable for this course is available on the UQ Public Timetable.

Additional timetable information

Classes and practicals will be conducted on campus.ﾠConsult your personal timetable for times and locations.ﾠStudents are expected to attend these sessions in person,ﾠ unless they have a valid reason for being unable to attend (such as illness).ﾠ

Aims and outcomes

This is a course on the qualitative methods for ordinary differential equations and dynamical systems.

The aims of this course are (i) to learn and understand these methods, (ii) to apply them to gain an in-depth understanding of models from mathematics, natural sciences and engineering, and (iii) to be able to communicate the results using mathematical and computational resources in a clear, relevant and coherent way.

After successfully completing this course you should understand and be able to apply a range of techniques as outlined below, and successfully communicate your results and findings.ﾠ

Learning outcomes

After successfully completing this course you should be able to:

Assessment

Assessment summary

A hurdle is an assessment requirement that must be satisfied in order to receive a specific grade for the course. Check the assessment details for more information about hurdle requirements.

Assessment details

Assignments

• Online

Mode

Written

Category

Computer Code, Tutorial/ Problem Set

Weight

36%

Due date

25/03/2025 4:00 pm

29/04/2025 4:00 pm

27/05/2025 4:00 pm

Assignments are due on Tuesday at 4pm on the corresponding week. Assignment 1 is worth 10%. Assignment 2 is worth 12% . Assignment 3 is worth 14%.

Learning outcomes

L01, L02, L03, L04, L05, L06

Task description

Submission guidelines

Assignments will be submitted electronically (as a single pdf file) using Gradescope, by the specified time on the due date.

Deferral or extension

You may be able to apply for an extension.

The maximum extension allowed is 7 days. Extensions are given in multiples of 24 hours.

Solutions for assessment item/s will be released one week after the assessment is due and as such, an extension after 7 days will not be possible.

See ADDITIONAL ASSESSMENT INFORMATION for further extension/deferral information relating to this assessment item.

Late submission

A penalty of 10% of the maximum possible mark will be deducted per 24 hours from time submission is due for up to 7 days. After 7 days, you will receive a mark of 0.

You are required to submit assessable items on time. If you fail to meet the submission deadline for any assessment item then the listed penalty will be deducted per day for up to 7 calendar days, at which point any submission will not receive any marks unless an extension has been approved. Each 24-hour block is recorded from the time the submission is due.

Quiz 1

• In-person

Mode

Activity/ Performance, Written

Category

Quiz

Weight

6%

Due date

Monday Week 7, completed during second lecture.

Other conditions

Time limited.

See the conditions definitions

Learning outcomes

L01, L02, L03

Task description

Submission guidelines

Quizzes will be completed in-person during lecture time, and due by the end of the lecture.

Deferral or extension

You may be able to defer this exam.

If, on approved grounds for an extension, a student is unable to sit a quiz, then they will qualify for a deferred assessment. A deferred assessment may consist of a combination of oral and written components, and must be taken at a specific time, informed to the student by the SMP student admin team.

See ADDITIONAL ASSESSMENT INFORMATION for further extension/deferral information relating to this assessment item.

Late submission

Late submissions will NOT be accepted.

Quiz 2

• In-person

Mode

Activity/ Performance, Written

Category

Quiz

Weight

6%

Due date

Tuesday Week 12, completed during lecture time.

Other conditions

Time limited.

See the conditions definitions

Learning outcomes

L04, L05, L06

Task description

Submission guidelines

Quizzes will be completed in-person during lecture time, and due by the end of the lecture.

Deferral or extension

You may be able to defer this exam.

If, on approved grounds for an extension, a student is unable to sit a quiz, then they will qualify for a deferred assessment. A deferred assessment may consist of a combination of oral and written components, and must be taken at a specific time, informed to the student by the SMP student admin team.

See ADDITIONAL ASSESSMENT INFORMATION for further extension/deferral information relating to this assessment item.

Late submission

Late submissions will NOT be accepted.

Two-hour invigilated exam

• Hurdle
• In-person

Mode

Written

Category

Examination

Weight

52%

Due date

End of Semester Exam Period

7/06/2025 - 21/06/2025

Learning outcomes

L01, L02, L03, L04, L05, L06

Task description

Hurdle requirements

Exam details

Submission guidelines

Deferral or extension

You may be able to defer this exam.

Course grading

Full criteria for each grade is available in the Assessment Procedure.

Additional course grading information

Note that there are final exam hurdles, detailed in the Course grading descriptions.

Supplementary assessment

Supplementary assessment is available for this course.

Should you fail a course with a grade of 3 you may be eligible for supplementary assessment. Refer to my.UQ for information on supplementary assessment and how to apply.

Supplementary assessment provides an additional opportunity to demonstrate you have achieved all the required learning outcomes for a course. If you apply and are granted supplementary assessment, the type of supplementary assessment set will consider which learning outcome(s) have not been met.

Supplementary assessment in this course will be an examination similar in style to the end- of-semester examination. To receive a passing grade of 3S4, you must obtain a mark of 50% or more on the supplementary assessment.

Additional assessment information

Artificial Intelligence

Assessment tasks in this course evaluate students' abilities, skills and knowledge without the aid of generative Artificial Intelligence (AI) or Machine Translation (MT). Students are advised that the use of AI or MT technologies to develop responses is strictly prohibited and may constitute student misconduct under the Student Code of Conduct.

Applications for Extensions to Assessment Due Dates and Deferred Quizzes

Extension/quiz deferral requests are submitted online via my.UQ – applying for an extension. Extension/quiz deferral requests received in any other way will not be approved. Additional details associated with extension requests, including acceptable and unacceptable reasons, may be found at my.UQ.

Please note:

• Requests for an extension to an assessment due date must be submitted through your my.UQ portal and you must provide documentation of your circumstances, as soon as it becomes evident that an extension is needed. Your application must be submitted on or before the assessment item's due date and time.
• Applications for extension can take time to be processed so you should continue to work on your assessment item while awaiting a decision. We recommend that you submit any completed work by the due date, and this will be marked if your application is not approved. Should your application be approved, then you will be able to resubmit by the agreed revised due date.
• If an extension is approved, you will be notified via your my.UQ portal and the new date and time for submission provided. It is important that you check the revised date as it may differ from the date that you requested.
• If the basis of the application is a medical condition, applications should be accompanied by a medical certificate dated prior to the assignment due date. If you are unable to provide documentation to support your application by the due date and time you must still submit your application on time and attach a written statement (Word document) outlining why you cannot provide the documentation. You must then upload the documentation to the portal within 24 hours.
• If an extension is being sought on the basis of exceptional circumstances, it must be accompanied by supporting documentation (eg. Statutory declaration).
• For extensions based on a SAP you may be granted a maximum of 7 days (if no earlier maximum date applies). See the Extension or Deferral availability section of each assessment for details. Your SAP is all that is required as documentation to support your application. However, additional extension requests for the assessment item will require the submission of additional supporting documentation e.g., a medical certificate. All extension requests must be received by the assessment due date and time.
• Students may be asked to submit evidence of work completed to date. Lack of adequate progress on your assessment item may result in an extension being denied.
• If you have been ill or unable to attend class for more than 14 days, you are advised to carefully consider whether you are capable of successfully completing your courses this semester. You might be eligible to withdraw without academic penalty - seek advice from the Faculty that administers your program.
• There are no provisions to defer a deferred quiz. You need to be available to sit your deferred quiz.
• There are no provisions for exemption from an assessment item within UQ rules. If you are unable to submit an assessment piece then, under special circumstances, you may be granted an exemption, but may be required to submit alternative assessment to ensure all learning outcomes are met.

Applications to defer an exam

In certain circumstances you can apply to take a deferred examination for in-semester and end-of-semester exams. You'll need to demonstrate through supporting documentation how unavoidable circumstances prevented you from sitting your exam. If you can’t, you can apply for a one-off discretionary deferred exam.

Deferred Exam requests are submitted online via mySi-net. Requests received in any other way will not be approved. Additional details associated with deferred examinations, including acceptable and unacceptable reasons may be found at my.UQ.

Please note:

• Applications can be submitted no later than 5 calendar days after the date of the original exam.
• There are no provisions to defer a deferred exam. You need to be available to sit your deferred examination.
• Your deferred examination request(s) must have a status of "submitted" in mySI-net to be assessed.
• All applications for deferred in-semester examinations are assessed by the relevant school. Applications for deferred end-of-semester examinations are assessed by the Academic Services Division.
• You’ll receive an email to your student email account when the status of your application is updated.
• If you have a medical condition, mental health condition or disability and require alternative arrangements for your deferred exam you’ll need to complete the online alternative exam arrangements through my.UQ. This is in addition to your deferred examinations request. You need to submit this request on the same day as your request for a deferred exam or supplementary assessment. Contact Student Services if you need assistance completing your alternative exam arrangements request.

Learning resources

You'll need the following resources to successfully complete the course. We've indicated below if you need a personal copy of the reading materials or your own item.

Library resources

Find the required and recommended resources for this course on the UQ Library website.

Additional learning resources information

Required Resources

Tutorial Sheets and other course materials will be available online via Blackboard. Please make sure you visit the course Blackboard website often throughout the semester.

Make sure you have access to and read the following books.

• Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering, by S. Strogatz. Westview Press, 2014.

Online at UQ: http://www.uql.eblib.com.au.ezproxy.library.uq.edu.au/patron/FullRecord.aspx?p=1181622&echo=1&userid=uJinVEXycVZ7v7FehDV1qyj7XbdaTB3Y&tstamp=1453437496&id=9FC56E71E09392D53B54FF5DA24072D1A25300C4

• Stability, Instability and Chaos, by P. Glendinning, Cambridge University Press.

Online at UQ: http://ebooks.cambridge.org.ezproxy.library.uq.edu.au/ebook.jsf?bid=CBO9780511626296

Recommended Resources

• Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, J. Guckenheimer and P. Holmes, Applied Mathematical Sciences vol 42, Springer, 1983.

http://link.springer.com/book/10.1007/978-1-4612-1140-2

• Chaos, an introduction to Dynamical Systems, K.T. Alligood, T.D. Sauer, J.A. Yorke, Springer, 1996.

http://link.springer.com/book/10.1007/b97589

• The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors, C. Sparrow, Applied Mathematical Sciences 41, Springer, 1982.

http://link.springer.com/book/10.1007/978-1-4612-5767-7

• A Guide to Matlab For Beginners and Experienced Users 2nd edition

Brian R. Hunt,  Ronald L. Lipsman , Jonathan M. Rosenberg , Kevin R. Coombes , John E. Osborn, , Garrett J. Stuck

https://www-cambridge-org.ezproxy.library.uq.edu.au/core/books/guide-to-matlab/CEC178067B0D5734E3F172FBE6777955

https://www-cambridge-org.ezproxy.library.uq.edu.au/core/books/guide-to-matlab/CEC178067B0D5734E3F172FBE6777955

• Exploring ODEs

Lloyd N. Trefethen, Ásgeir Birkisson, Tobin A. Driscoll

http://people.maths.ox.ac.uk/trefethen/Exploring.pdf

Learning activities

The learning activities for this course are outlined below. Learn more about the learning outcomes that apply to this course.

Policies and procedures

University policies and procedures apply to all aspects of student life. As a UQ student, you must comply with University-wide and program-specific requirements, including the:

• Student Code of Conduct Policy
• Student Integrity and Misconduct Policy and Procedure
• Assessment Procedure
• Examinations Procedure
• Reasonable Adjustments - Students Policy and Procedure

Learn more about UQ policies on my.UQ and the Policy and Procedure Library.