MATH4021 Dynamical Systems

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)]
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.
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.

Supplementary assessment is not available in this unit.
Unit Coordinator(s)
Professor Michael Small
Unit rules
MATH3021 Nonlinear Dynamics and Chaos (formerly Dynamics and Control)
Contact hours
3 hours per week
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  • Books and other material wherever listed may be subject to change. Book lists relating to 'Preliminary reading', 'Recommended reading' and 'Textbooks' are, in most cases, available via the Booktopia Textbook Finder, which has the functionality to search by course code, course, ISBN and title, and may also be posted or available at the appropriate school's administrative offices. Where texts are listed in the unit description above, an asterisk (*) indicates that the book is available in paperback.