| Course Description | Nonlinear systems, phase portraits, equilibria and stabilities. Birfurcation theory. Global properties. Gradient systems and Hamiltonian systems. Lyapunov functions. Closed orbits and limit cycles. Poincare maps. The Poincare-Bendixson Theorem. The Lorenz system. Strange attractors. Concept of chaos. Discrete dynamical systems, the shift map, the Cantor set, conept of fractals. Applications in mechanics, chemistry, and biology. |
| Prerequisites | Math 130A or consent of instructor. |
| Textbook |
M. W. Hirsch, S. Smale, and R. L Devaney, Differential Equations, Dynamical Systems & An Introduction to Chaos, 3rd ed., Elsevier, 2013.
(We will cover chapters 8 - 10, 14, and 15, and some part of chapters 11 and 12 of applications.)
Other main references: |
| Matlab | We will use pplane8.m for ploting director fields and phase portraits for planar systems. |
| Lectures | 10:00 am - 10:50 am, Mondays, Wednesdays, and Fridays, AP&M 5829. |
| Instructor | Professor Bo Li. Office: AP&M 5723. Phone: (805) 534-6932. Email: bli@math.ucsd.edu. Office hours: 11:00 - 11:30 Mondays and 11:00 - 11:30 Wednesdays, or by appointment. |
| Discussion Session | 8:00 am - 8:50 am, Tuesdays, AP&M B412. |
| Teaching Assistant |
Mr. Benjamin Ciotti. Office: AP&M 5712. Email: bciotti@ucsd.edu.
Office hours: 5:00 pm - 5:50 pm, Mondays and 11:00 am - 11:50 am, Fridays. |
| Homework |
Homework will be assigned, collected in class, and partially graded regularly.
The program pplane8.m can be used to plot phase portraits.
Note: no late homework will be accepted unless a written verification of a valid excuse (such as hospitalization, family emergency, religious observance, court appearance, etc.) is provided. |
| Exams |
There will be one midterm and one final, close-book and close-note exams.
No calculators will be allowed in these exams. The final exam will be cumulative.
Midterm Exam: 10:00 am - 10:50 am, Friday, May 3, 2019, AP&M 5829. Final Exam: 8:00 am - 11:00 am, Monday, June 10, 2015, AP&M 5829. Note: neither rescheduled nor make-up exams will be allowed unless a written verification of a valid excuse (such as hospitalization, family emergency, religious observance, court appearance, etc.) is provided. |
| Grading | The final course grade will be determined based on the homework and exams with the weights: class participation 5%, homework - 20%, midterm exam - 30%, and the final exam - 45%. The grades will be curved. |