Math 3100
Introduction to Dynamical Systems

Winter, 2023

Text: Steven H. Strogatz, "Nonlinear Dynamics and Chaos", Westview Press, Perseus Books Publishing, 1994.

Prerequisite: Math 2260

Evaluation:

Course Contents:

• First-Order Equations (Chapter 2)
  • The Simplest Example
  • The Logistic Population Model
  • Linear Stability Analysis
• Bifurcations (Chapter 3)
  • Saddle-Node Bifurcation
  • Transcritical Bifurcation
  • Pitchfork Bifurcation
• Linear Systems (Chapter 5)
  • Definitions and Examples
  • Classification of Linear Systems
• Phase Plane (Chapter 6)
  • Phase Portraits
  • Linearization
  • A Lotka-Volterra Competition Model (Rabbits versus Sheep)
• Limit Cycles (Chapter 7)
  • Definition and Examples
  • Ruling Out Closed Orbits
  • Poincare-Bendixson Theorem
• Bifurcations Revisited (Chapter 8)
  • Saddle-Node,Transcritical, Pitchfork Bifurcations
  • Hopf Bifurcations
  • Global Bifurcations of Cycles
• Discrete Dynamical Systems (Chapter 10)
  • Fixed Points and Cobwebs
  • Logistic Map
  • Chaos
• Conservative Systems (Chapter 6)

  Assignments:

  Assignments are to be dropped into the mailbox #43 (Henrietta Harvey Building) at any time on the due date. No late assignments are acceptable.

  Assignment 1 (Due date: Monday, Jan. 23):

  Exercises 2.2.7, 2.3.4, 2.4.5, 2.4.7; and Exercises 3.1.1, 3.1.4, 3.2.2, 3.4.1, 3.4.14
  Here are the PDF files of Exercises (Chapter 2) and Exercises (Chapter 3)
  Solution to HW1

  Assignment 2 (Due date: Monday, Jan. 30):

  Due to the strike happening on Jan. 30, the due date of HW2 is Wed., Feb. 15

  Exercises 5.1.2, 5.1.9, 5.1.10, 5.2.1, 5.2.12
  Here is the PDF file of Exercises (Chapter 5)
  Solution to HW2

  Assignment 3 (Due date: Monday, Feb.27):

  Exercises 6.1.5, 6.3.1, 6.3.11, 6.3.14,6.4.2
  Here is the PDF file of Exercises (Chapter 6)
  Solution to HW3

  Assignment 4 (Due date: Wednesday, March 15):

  Exercises 7.1.2, 7.1.8, 7.2.6 b), 7.2.12, 7.2.13, 7.3.4
  Here is the PDF file of Exercises (Chapter 7)
  Solution to HW4

  Assignment 5 (Due time: 5:00pm, Friday, March 24):

  Exercises 8.1.1, 8.1.6, 8.2.1, 8.2.6
  Here is the PDF file of Exercises (Chapter 8)
  Solution to HW5

  Assignment 6, Due time: 5:00pm, Wednesday, April 5

  Solution to HW6

  Midterm Test (in the classroom): 2:00pm-2:50pm, Monday, March 6

  The midterm test covers the contents discussed in ALL classes before and on March 3
  Solution to Midterm Test

  Final Exam: 12:00-14:30, Monday, April 17, SN-3060