Kaitlin Hill
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Discrete Dynamical Systems
MST 354/654
Spring 2022

Objectives: 
​During this course, students will develop their skills in analyzing discrete dynamical systems. These skills include:
  • Solving one- and two-dimensional discrete dynamical systems
  • Graphically analyzing fixed points of discrete dynamical systems and their stability
  • Interpreting a discrete dynamical systems model in a given application, primarily in population dynamics, economics, and biology
  • Understanding and describing chaotic behavior in a discrete dynamical system
To attain these objectives, we will learn the about following mathematical topics:
  • Chapter 1: Stability of one-dimensional maps
  • Chapter 3: Chaos in one dimension
  • Chapter 4: Stability of two-dimensional maps
  • Chapter 5: Chaos in two dimensions
Picture
The chaotic attractor for the Duffing equation
Textbook: Discrete Chaos, by Saber Elaydi
​Supplemental text: Dynamical Systems in Economics Lecture Notes, by Miaohua Jiang

Course Documents and Links:
Syllabus
Course Spreadsheet / Record
Homework guidelines
Canvas
Final exam topics

Class Notes:
  • Week 1: Sections 1.1 - 1.2
  • Week 2: Sections 1.3 - 1.6
    • Worksheet 2 notes
  • Week 3: Sections 1.7 - 1.8 
    • Worksheet 4 notes
  • Week 5: Worksheet 5 notes
  • Week 6: Sections 1.7 - 1.9
  • Week 7: Section 1.9
    • Logistic map code notes
  • Week 8: Section 2.5
  • Week 10: Section 2.5
  • Week 11: Section 2.5 and 4.12
  • Week 12: Sections 4.5 and 4.7
  • Week 13: Sections 4.8 and 4.1

Worksheets:
  • Worksheet 1: Section 1.2
  • Worksheet 2: Section 1.5
  • Worksheet 3: Section 1.6 - 1.7
  • Worksheet 4: Section 1.8
  • Worksheet 5: Section 1.8
  • Worksheet 6: Section 1.9
  • Worksheet 7: Section 2.5
  • Worksheet 8: Section 4.12
​
Homework:
  • ​​Homework 1 (solutions)
  • Homework 2 (solutions)
  • Homework 3 (solutions)
  • Homework 4 (solutions)
  • Homework 5 (solutions, code)
  • Homework 6 (solutions, code)
  • Homework 7 (solutions, code)
  • Homework 8
​
Code:
  • Mortgage loan minimum payment.nb
  • Euler's Method.nb
  • Logistic map.nb
  • Henon map.nb
  • Baker map.nb
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  • Home
  • CV
  • Research
    • Student projects
  • Publications
  • Teaching
    • Geogebra
    • MST 251
    • MST 354/654
  • Outreach