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Unit of study_

MATH4414: Advanced Dynamical Systems

In applied mathematics, dynamical systems are systems whose state is changing with time. Examples include the motion of a pendulum, the change in the population of insects in a field or fluid flow in a river. These systems are typically represented mathematically by differential equations or difference equations. Dynamical systems theory reveals universal mechanisms behind disparate natural phenomena. This area of mathematics brings together sophisticated theory from many areas of pure and applied mathematics to create powerful methods that are used to understand and control the dynamical building blocks which make up physical, biological, chemical, engineered and even sociological systems. By doing this unit you will develop a broad knowledge of methods and techniques in dynamical systems, and know how to use these to analyse systems in nature and in technology. This will provide a strong foundation for using mathematics in a broad sweep of applications and for research or further study.

Code MATH4414
Academic unit Mathematics and Statistics Academic Operations
Credit points 6
Assumed knowledge:
Assumed knowledge is vector calculus (e.g., MATH2X21), linear algebra (e.g., MATH2X22), dynamical systems and applications (e.g., MATH4063 or MATH3X63) or equivalent. Some familiarity with partial differential equations (e.g., MATH3978) and mathematical computing (e.g., MATH3976) is also assumed.

At the completion of this unit, you should be able to:

  • LO1. Understand the distinction between continuous, discrete, and finite dynamical systems.
  • LO2. Understand the concept of transfer and composition operators.
  • LO3. Explain how the single and double pendulum are important paradigms for much of general dynamical systems.
  • LO4. Be able to gain intuition about a system by computing examples numerically.
  • LO5. Understand bifurcations, period doubling, and transition to chaos,
  • LO6. Understand the statistical nature of ensembles of deterministic and stochastic solutions to dynamical systems.

Unit outlines

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