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.
|Unit name||Dynamical Systems and Chaos|
|College/School||College of Sciences and Engineering
School of Natural Sciences
|Coordinator||Doctor Courtney Quinn|
|Available as an elective?||Yes|
|Delivered By||University of Tasmania|
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- 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.
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PrerequisitesAdmission into a relevant Masters course OR (KMA252 and KMA254) OR (KYA211 and KYA212) OR (KYA375 - Engineering Physics AND KME271 - Engineering Mathematics)
3 x 50 minute lectorials weekly, 1 x 50 minute workshop weekly, 1 x 2 hour optional computer lab drop-in session weekly
|Assessment||Oral exam (10%)|Project (20%)|Assignments (30%)|Examination (40%)|
|Timetable||View the lecture timetable | View the full unit timetable|
Required readings will be listed in the unit outline prior to the start of classes.
|Links||Booktopia textbook finder|
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