Quick Links:
Instructor:
Ralf Wittenberg
K-10536, 291-4792
ralf@sfu.ca |
Lectures:
M 2:30-3:20pm
W 2:30-4:20pm
in AQ 4130 |
Text:
Steven Strogatz,
Nonlinear Dynamics and Chaos
Westview Press |
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Announcements:
- Lecture 10: 6 October
Nonuniform Oscillators:
Oscillation period, ghosts and bottlenecks, square-root scaling, overdamped pendulum
Reading: Strogatz Ch.4 (4.3, 4.4) - also read 4.5 and 4.6 if you are interested; lecture notes
- Homework Set 4
- Suggested additional exercises for this lecture (optional):
4.3.1, 4.3.2, 4.3.3, 4.3.9, 4.4.1
- Lecture 11: 8 October
One-dimensional Maps:
Iterative maps, fixed points and stability, periodic orbits, cobwebs; the logistic map, transcritical bifurcation, period-doubling bifurcation sequence to chaos
Reading: Strogatz Ch.10 (10.0, 10.1, 10.2, 10.3), lecture notes
- Homework Set 5
Note: the material for some of the questions from 10.3 will be covered in lecture 12 on 15 October; the homework is due several days later.
- Matlab code:
- logist1.m Iterate logistic map, plot iterates vs n
- logistic_cobweb.m Cobweb construction for logistic map
- logistic_cobweb2.m Cobwebs for logistic map, without transients
- logistic_orbit.m Orbit diagram for logistic map
- logistic_lyapunov.m Lyapunov exponents for logistic map
- Code to iterate general functions f:
Sample function m-files: f.m (logistic map), sinfun.m (sine map) with corresponding derivatives df.m, dsinfun.m
Composition of functions (2nd, 3rd, 4th iterate maps): f2.m, f3.m, f4.m
Iterate functions without parameters - iterates vs n: iter1.m, iter1x.m
- cobweb diagrams: iter2.m, iter2x.m
Iterate functions with parameters: iterp1.m, iterp2.m, iterp3.m
Orbit diagram: iter_orbit.m
Lyapunov expondents: iter_lyapunov.m
- Suggested additional exercises for this lecture (optional):
10.1.2, 10.1.6, 10.1.9, 10.1.10, 10.2.1, 10.2.2, 10.2.7, 10.2.8
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