Studying online

There are now 2 possible online modes for units:

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Unit Overview


This unit delves into the meaning of chaos and the implications it has for modelling reality. Topics may include (1) probabilistic properties of deterministic systems—chaos is not randomness, but probability theory can be used to provide useful characterisations of chaos; (2) structural stability—under what conditions will a model of a system have essentially the same dynamics as the system, taking into account that the model will have some degree of error?; (3) shadowing—how do we find the 'true' trajectory when we are given only noisy observations?; (4) embedding—if we only know that a system has a finite number of variables (that is, it is a finite dimensional map or flow) but do not know how many, then how many different quantities should we measure to completely discover the dynamics? The surprising answer is that usually only one is necessary; and (5) nonlinear time series analysis—how to use information theory to build a model of the dynamics of a system.

6 points
(see Timetable)
Semester 1UWA (Perth)Face to face
Details for undergraduate courses
  • Level 4 elective
  • Honours option in Mathematics and Statistics [Bachelor of Science (Honours)]

Students are able to (1) demonstrate an awareness of modern techniques appropriate to the understanding of complex dynamical systems, including (but not limited to)—embedding and reconstruction, modelling and information, dynamical invariants, shadowing and filtering, and/or nonlinear Monte Carlo hypothesis testing; (2) demonstrate knowledge of tolls and techniques appropriate to the application of these methods; (3) understand the theoretical underpinnings of these techniques; and (4) appropriately apply these techniques to experimental time series data obtained from deterministic low-dimensional dynamical systems.


Indicative assessments in this unit are as follows: (1) project and (2) assignments. Further information is available in the unit outline.

Student may be offered supplementary assessment in this unit if they meet the eligibility criteria.

Unit Coordinator(s)
Professor Michael Small
Unit rules
Enrolment in
in the HON-MTHST Mathematics and Statistics [Honours]
and MATH3021 Nonlinear Dynamics and Chaos
Contact hours
3 hours per week
  • The availability of units in Semester 1, 2, etc. was correct at the time of publication but may be subject to change.
  • All students are responsible for identifying when they need assistance to improve their academic learning, research, English language and numeracy skills; seeking out the services and resources available to help them; and applying what they learn. Students are encouraged to register for free online support through GETSmart; to help themselves to the extensive range of resources on UWA's STUDYSmarter website; and to participate in WRITESmart and (ma+hs)Smart drop-ins and workshops.
  • Unit readings, including any essential textbooks, are listed in the unit outline for each unit, one week prior the commencement of study. The unit outline will be available via the LMS and the UWA Handbook one week prior the commencement of study. Reading lists and essential textbooks are subject to change each semester. Information on essential textbooks will also be made available on the Essential Textbooks. This website is updated regularly in the lead up to semester so content may change. It is recommended that students purchase essential textbooks for convenience due to the frequency with which they will be required during the unit. A limited number of textbooks will be made available from the Library in print and will also be made available online wherever possible. Essential textbooks can be purchased from the commercial vendors to secure the best deal. The Student Guild can provide assistance on where to purchase books if required. Books can be purchased second hand at the Guild Secondhand bookshop (second floor, Guild Village), which is located on campus.
  • Contact hours provide an indication of the type and extent of in-class activities this unit may contain. The total amount of student work (including contact hours, assessment time, and self-study) will approximate 150 hours per 6 credit points.