Handbook 1996 : Faculty of Science (Volume 4 page 214)
Mathematics subject : Next:618-342 | Prev:618-340 | Search | Help
618-341 "Dynamical Systems and Chaos" appears differently in several places - choose the one you want:
1. Mathematics, Faculty of Science (v4, p214) : Next:618-342 | Prev:618-340
Credit points: 15.0
Coordinator: Professor C J Thompson
Prerequisite: Mathematics 618-130 or 618-132 together with one of 618-201, 618-231, 618-232, 618-252.
Contact: 39 lectures (three a week).
Timetable: First semester.
Objectives:
On completion of this subject, students should:Comprehend:
- the basic concepts and recent developments in the fields of dynamical systems and chaos, including stability of equilibria and renormalization theory of transitions to chaos.
Have developed:
- the ability to analyse simple nonlinear discrete and continuous dynamical systems, and to chart parameter regions of stability, periodicity and chaos.
Appreciate:
- the power as well as the limitations of dynamical systems theory and chaos applied to realistic complex systems such as ecologies and financial markets.
Content:
Dynamical systems:phase space, Poincare sections, phase portraits, Hamiltonian systems, invariant measures. Chaos:integrable and chaotic systems, maps on an interval, period doubling and universality, renormalisation and scaling, reversible mappings, KAM theorems, strange attractors, fractals, limit cycles, Hopf bifurcation, Lorentz attractor, Lyapunov exponents, dimensions of strange attractors, hierarchies of chaos, applications to ecology, chemical reactions, economics, management and meteorology.
Assessment:
Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.
1. Mathematics, Faculty of Science (v4, p214) : Next:618-342 | Prev:618-340
2. Math. & Stats., Faculty of Educ(Parkville) (v5, p149) : Next:618-342 | Prev:618-340
Credit points: 15.0
Coordinator: Professor C J Thompson.
Prerequisite: Mathematics 618-130 or 618-132 together with one of 618-201, 618-231, 618-232, 618-252.
Contact: 39 lectures (three each week)
Timetable: First semester.
Objectives:
On completion of this subject, students should:Comprehend:
- the basic concepts and recent developments in the fields of dynamical systems and chaos, including stability of equilibria and renormalization theory of transitions to chaos.
Have developed:
- the ability to analyse simple nonlinear discrete and continuous dynamical systems, and to chart parameter regions of stability, periodicity and chaos.
Appreciate:
- the power as well as the limitations of dynamical systems theory and chaos applied to realistic complex systems such as ecologies and financial markets.
Content:
Dynamical systems Phase space, Poincare sections, phase portraits, Hamiltonian systems, invariant measures. Chaos Integrable and chaotic systems, maps on an interval, period doubling and universality, renormalisation and scaling, reversible mappings, KAM theorems, strange attractors, fractals, limit cycles, Hopf bifurcation, Lorentz attractor, Lyapunov exponents, dimensions of strange attractors, hierarchies of chaos, applications to ecology, chemical reactions, economics, management and meteorology.
Assessment:
Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.
* Note that CONTACT, CONTENT differs from the maintainer's version above. A log of variations is available.
2. Math. & Stats., Faculty of Educ(Parkville) (v5, p149) : Next:618-342 | Prev:618-340
Status: Official 1996 Date created: Oct 9 1995 Last modified: Oct 9 1995 Authorised by: Academic Registrar Email enquiries: Course_Information@registrar.unimelb.edu.au
Maintained by: Dept. of Mathematics, Faculty of Science.
Copyright © University of Melbourne 1995,1996.