Fall 1999

M 540 : Dynamical Systems


Section:  1
Time:  11-12:15 TR
Meeting Room:  EE203
Instructor:  Gerhard Dangelmayr
Office:  EE217
Phone:  491-6451
Email:  gerhard@math.colostate.edu
Office Hours: 10 - 11:30 W, 12:30 - 2 R
Text: Nonlinear Dynamics and Chaos
by Steven H. Strogatz
Course Outline: 
CONTENTS:
Linear and nonlinear systems of ordinary differential equations;
geometric approach to dynamical systems (vector fields and 
iterated maps); bifurcations; aspects of chaotic dynamics;
physical, chemical and biological models. 

I. 1-Dimensional Flows:
Basic concepts, linear vs. nonlinear systems,
linearization. Steady state bifurcations: saddle node, 
transcritical, pitchfork and imperfect bifurcations.
Flows on circles and infinite period bifurcations.

II. 2-Dimensional Flows:
Classification of linear systems, phase space analysis, 
conservative and reversible systems. Limit cycles, relaxation 
oscillators vs. weakly nonlinear oscillators. Steady state 
bifurcations in 2-d, Hopf bifurcation. Coupled oscillators, 
Poincare maps. 

III. Chaos:
Lorenz equations, Lorenz map and its dependence on parameters. 
1-dimensional maps: Liapunov exponents, renormalization. 
Fractals: Cantor sets and fractal dimension.  
Examples of strange attractors.

Examinations: 
Homework with optional final.

Grading Policy:
If a final is taken it counts 40%, otherwise the grading will be based purely on homework.