MATH401-22S1 (C) Semester One 2022

Dynamical Systems

15 points

Details:
Start Date: Monday, 21 February 2022
End Date: Sunday, 26 June 2022
Withdrawal Dates
Last Day to withdraw from this course:
  • Without financial penalty (full fee refund): Sunday, 6 March 2022
  • Without academic penalty (including no fee refund): Sunday, 15 May 2022

Description

Dynamical Systems

Dynamical systems sits at the interface of pure and applied mathematics, containing some beautiful theory, as well as applications in diverse fields including numerical analysis, biological systems, economics and medicine.

It is often difficult or impossible to write down an exact solution to systems of nonlinear equations. The emphasis in this course will be on qualitative techniques for classifying the behaviour of nonlinear systems, without necessarily solving them exactly. Two main types of dynamical systems
will be studied: discrete systems, consisting of an iterated map; and continuous systems, consisting of nonlinear differential equations.

Topics covered will include: bifurcations and chaotic behaviour of interval maps; symbolic dynamics; topological model of chaos; mass transport and probabilistic dynamics; phase portrait analysis (Hartman-Grobman theorem, hyperbolicity of limit cycles, invariant manifolds, global bifurcations); centre manifolds.

This course is independent of MATH363 Dynamical Systems, although previous enrolment
there is desirable.

Learning Outcomes

  • To demonstrate a breadth of knowledge of dynamical systems theory traversing smooth, continuous and probabilistic settings and to apply that knowledge correctly in new situations
  • To be able to articulate what it means for a dynamical system to be chaotic, including the relation to randomness
  • To choose and apply appropriate theoretical and numerical tools to analyse a given dynamical system and communicate clear and correct explanations of its global asymptotic behaviour
  • To exhibit mastery of both the power and limitations of standard methods of linearisation, analysis via invariant manifolds and symbolic dynamics
  • To evaluate critically the findings and discussions in relevant original literature, and to exhibit familiarity with content that is relevant to the syllabus, but sits outside it
  • To engage in rigorous investigation and analysis of problems in dynamical systems both independently and collaboratively

      • University Graduate Attributes

      This course will provide students with an opportunity to develop the Graduate Attributes specified below:

      Critically competent in a core academic discipline of their award

      Students know and can critically evaluate and, where applicable, apply this knowledge to topics/issues within their majoring subject.

      Employable, innovative and enterprising

      Students will develop key skills and attributes sought by employers that can be used in a range of applications.

Prerequisites

Subject to approval of the Head of School.

Course Coordinator / Lecturer

Rua Murray

Indicative Fees

Domestic fee $1,017.00

* All fees are inclusive of NZ GST or any equivalent overseas tax, and do not include any programme level discount or additional course-related expenses.

For further information see Mathematics and Statistics .

All MATH401 Occurrences

  • MATH401-22S1 (C) Semester One 2022
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