Spring 2023 - MATH 767 G100
Dynamical Systems (3)
Class Number: 5321
Delivery Method: In Person
Course Times + Location:
Mo, We, Fr 12:30 PM – 1:20 PM
WMC 2830, Burnaby
Exam Times + Location:
Apr 13, 2023
3:30 PM – 6:30 PM
BLU 10921, Burnaby
1 778 782-4544
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.
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.
- Homework (Best 5 of 6) 20%
- In-class worksheets 10%
- Weekly Note Summaries (Best 10 out of 12) 10%
- Midterm test 35%
- Final Poster project 15%
Students enrolled in MATH 767 will be expected to submit an additional written project on a topic agreed upon with the instructor. The grading distribution will be as above except now the in-class worksheets will count for 10% and the report the remaining 10%.
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 + 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).
Nonlinear Dynamics and Chaos: with Applications to Physics, Biology, Chemistry, and Engineering, Steven Strogatz, Westview Press, 2015, 2nd Edition.
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.
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