MATHS543-20A (HAM)

Nonlinear Dynamics and Chaos

15 Points

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Division of Health Engineering Computing & Science
School of Computing and Mathematical Sciences
Department of Mathematics and Statistics

Staff

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Convenor(s)

Woei Chet Lim

Woei Chet Lim
5148
G.3.05
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woeichet.lim@waikato.ac.nz

Lecturer(s)

Administrator(s)

: maria.admiraal@waikato.ac.nz

Placement/WIL Coordinator(s)

Tutor(s)

Student Representative(s)

Lab Technician(s)

Librarian(s)

: debby.dada@waikato.ac.nz

You can contact staff by:

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Paper Description

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This paper introduces the students to nonlinear dynamics and chaos through analytical methods, examples and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by two-dimensional systems of first-order differential equations and their phase plane analysis, limit cycles and their bifurcations, culminating with the Lorenz equations – a three-dimensional system with chaotic behaviour and strange attractors. Iterated maps are used to illustrate chaos and fractals.

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Paper Structure

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Three lectures per week.
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Learning Outcomes

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Students who successfully complete the paper should be able to:

  • Analyse a dynamical systems qualitatively
    • Find fixed points and classify their stability
    • Sketch phase portraits
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  • Demonstrate understanding of the role of parameters in bifurcations
    • Find the value of parameter at which the bifurcation occurs
    • Classify the bifurcation
    • Sketch the bifurcation diagram
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  • Demonstrate understanding of limit cycles
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  • Demonstrate understanding of chaos as sensitive dependence on initial data
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  • Demonstrate understanding of fractals as complex geometric shapes with fine structure at arbitrarily small scales
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Assessment

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See assessment components below. Assignment due dates and test dates to be discussed with class.
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Assessment Components

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The internal assessment/exam ratio (as stated in the University Calendar) is 100:0. There is no final exam. The final exam makes up 0% of the overall mark.

The internal assessment/exam ratio (as stated in the University Calendar) is 100:0 or 0:0, whichever is more favourable for the student. The final exam makes up either 0% or 0% of the overall mark.

Component DescriptionDue Date TimePercentage of overall markSubmission MethodCompulsory
1. 10 weekly assignments
35
2. Test 1
15
3. Final test
50
Assessment Total:     100    
Failing to complete a compulsory assessment component of a paper will result in an IC grade
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Required and Recommended Readings

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Required Readings

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Nonlinear Dynamics and Chaos, by Steven H. Strogatz (Textbook will be provided.) (Q172.5.C45S767 2000)
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Recommended Readings

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Chaos: making a new science, by James Gleick (Q172.5.C45G54 1987)
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Other Resources

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Online Support

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Moodle.
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Workload

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10 hours per week.
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Linkages to Other Papers

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Prerequisite(s)

Prerequisite papers: (MATH311 or MATHS301) and (MATH255 or MATH259 or MATHS203)

Corequisite(s)

Equivalent(s)

Restriction(s)

Restricted papers: MATH543

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