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### MATH4021 Dynamical Systems

Credit
6 points
Offering
(see Timetable)
AvailabilityLocationMode
Semester 1UWA (Perth)Face to face
• Level 4 elective
• Honours option in Mathematics and Statistics [Bachelor of Science (Honours)]
Content
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.
Outcomes
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.
Assessment
Indicative assessments in this unit are as follows: (1) project and (2) assignments. Further information is available in the unit outline.

For units commencing in May 2022 or later the availability of the supplementary assessment is subject to confirmation.

Student may be offered supplementary assessment in this unit if they meet the eligibility criteria.
Unit Coordinator(s)
Professor Michael Small
Unit rules
Prerequisites:
Enrolment in in the HON-MTHST Mathematics and Statistics [Honours] and MATH3021 Nonlinear Dynamics and Chaos
Co-requisites:
Nil
Incompatibility:
Nil
Contact hours
3 hours per week
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• 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.