Nonlinear Dynamics I: Chaos
Lecture Notes
These lecture notes do not correspond to specific class sessions, and are organized by topic.
Full set of lecture notes (PDF - 1.7 MB)
Separate Files by Topics
Front Matter (table of contents, acknowledgements, and references) (PDF)
Pendulum (PDF)
Stability of Solutions to ODEs (PDF)
Conservation of Volume in Phase Space (PDF)
Damped Oscillators and Dissipative Systems (PDF)
Forced Oscillators and Limit Cycles (PDF)
Parametric Oscillator (PDF)
Fourier Transforms (PDF)
Poincare Sections (PDF)
Fluid Dynamics and Rayleigh-Benard Convection (PDF)
Introduction to Strange Attractors (PDF)
Lorenz Equations (PDF)
Henon Attractor (PDF)
Experimental Attractors (PDF)
Fractals (PDF)
Lyapunov Exponents (PDF)
Period Doubling Route to Chaos (PDF)
Intermittency (and Quasiperiodicity) (PDF)
Assignments
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ASSIGNMENTS |
ASSOCIATED READINGS |
SUPPLEMENTARY FILES |
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Problem Set 1 (PDF) |
Introduction to MATLAB® (PDF) Stark, J., and K. Hardy. "Chaos Useful at Last." Science 301, no. 5637 (August 29, 2003): 1192-1193. |
iterate.m (M) |
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Problem Set 2 (PDF) |
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Problem Set 3 (PDF) |
Solving ODEs on MATLAB® (PDF) |
vanderpol.m (M) |
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Problem Set 4 (PDF) |
The Driven Pendulum (PDF) (Courtesy of Jan M. Skotheim. Used with permission.) Tips on Analyzing Pendulum Data (PDF) |
makesignal.m (M) fourier.m (M) |
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Problem Set 5 (PDF) |
Damped Driven Pendulum (PDF) |
drvpend.m (M) drvpend.c (C) |
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Problem Set 6 (PDF) |
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Problem Set 7 (PDF) |
Lorenz Model (PDF) |
lorenz.m (M) |
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Problem Set 8 (PDF) |
Guide to Fracdim (PDF) |
(Makefile) fracdim.c (C) fracdim.m (M) correl.c (C) loaddat.m (M) |
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Problem Set 9 (PDF) |
Supplement to Problem Set 9 (PDF) |
iterate.m (M) |