Spring 2025 - MATH 467 D100

Dynamical Systems (3)

Class Number: 2785

Delivery Method: In Person

Overview

  • Course Times + Location:

    Jan 6 – Apr 9, 2025: Mon, Wed, Fri, 12:30–1:20 p.m.
    Burnaby

  • Instructor:

    Razvan Fetecau
    van@sfu.ca
    1 778 782-3335
  • Prerequisites:

    MATH 260 or MATH 310, with a minimum grade of C-.

Description

CALENDAR DESCRIPTION:

Stability and bifurcation in continuous and discrete dynamical systems, with applications. The study of the local and global behaviour of linear and nonlinear systems, including equilibria and periodic orbits, phase plane analysis, conservative systems, limit cycles, the Poincare-Bendixson theorem, Hopf bifurcation and an introduction to chaos. Quantitative.

COURSE DETAILS:

This is an introductory course to nonlinear dynamical systems and chaos. We will focus on qualitative properties of nonlinear systems and basic tools in analyzing these systems.
Topics for this course include:

  • Fixed points and limit cycles: local and global analysis including local stability analysis, the Poincaré-Bendixon theorem.
  • Bifurcations: normal form reduction, center manifold theorem, local bifurcations including various single-zero eigenvalue bifurcation and Poincaré-Andronov-Hopf bifurcation, and global bifurcations including homoclinic bifurcations.
  • Applications

Students will be expected to do short computations in matlab starting from distributed codes.

Grading

  • Homework 25%
  • Midterm test 20%
  • Final exam 55%

NOTES:

THE INSTRUCTOR RESERVES THE RIGHT TO CHANGE ANY OF THE ABOVE INFORMATION.

Students should be aware that they have certain rights to confidentiality concerning the return of course papers and the
posting of marks. Please pay careful attention to the options discussed in class at the beginning of the semester

Materials

MATERIALS + SUPPLIES:

This course is delivered in person, on campus. Should public health guidelines recommend limits on in person gatherings,
this course may include virtual meetings. As such, all students are recommended to have access to strong and reliable
internet, the ability to scan documents (a phone app is acceptable) and access to a webcam and microphone (embedded in
a computer is sufficient).

REQUIRED READING:

Nonlinear Dynamics and Chaos: with Applications to Physics, Biology, Chemistry, and Engineering, Steven Strogatz, Westview Press, 2015, 2nd Edition.
ISBN: 9780813349107

REQUIRED READING NOTES:

Your personalized Course Material list, including digital and physical textbooks, are available through the SFU Bookstore website by simply entering your Computing ID at: shop.sfu.ca/course-materials/my-personalized-course-materials.

Registrar Notes:

ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS

SFU’s Academic Integrity website http://www.sfu.ca/students/academicintegrity.html is filled with information on what is meant by academic dishonesty, where you can find resources to help with your studies and the consequences of cheating. Check out the site for more information and videos that help explain the issues in plain English.

Each student is responsible for his or her conduct as it affects the university community. Academic dishonesty, in whatever form, is ultimately destructive of the values of the university. Furthermore, it is unfair and discouraging to the majority of students who pursue their studies honestly. Scholarly integrity is required of all members of the university. http://www.sfu.ca/policies/gazette/student/s10-01.html

RELIGIOUS ACCOMMODATION

Students with a faith background who may need accommodations during the term are encouraged to assess their needs as soon as possible and review the Multifaith religious accommodations website. The page outlines ways they begin working toward an accommodation and ensure solutions can be reached in a timely fashion.