Spring 2025 - MATH 767 G100
Dynamical Systems (3)
Class Number: 2756
Delivery Method: In Person
Overview
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Course Times + Location:
Jan 6 – Apr 9, 2025: Mon, Wed, Fri, 12:30–1:20 p.m.
Burnaby
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Instructor:
Razvan Fetecau
van@sfu.ca
1 778 782-3335
Description
CALENDAR DESCRIPTION:
Stability and bifurcation in vector fields and discrete maps. Centre manifold theory and applications of normal forms. Introduction to chaos, Lyapunov exponents, and normal hyperbolicity.
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
The graduate students enrolled in Math 767 will be asked to perform some additional work (e.g., study independently extra graduate-level material and/or prepare and submit an additional assignment).
Materials
MATERIALS + SUPPLIES:
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
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.
Graduate Studies Notes:
Important dates and deadlines for graduate students are found here: http://www.sfu.ca/dean-gradstudies/current/important_dates/guidelines.html. The deadline to drop a course with a 100% refund is the end of week 2. The deadline to drop with no notation on your transcript is the end of week 3.
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.