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18.385 Nonlinear Dynamics and Chaos, Fall 2002

Phase Plane Portrait for the Dipole Fixed Point System for n = 1.
Phase Plane Portrait for the Dipole Fixed Point System for n = 1. (Image by Prof. Rosales adapted from the lecture notes)

Highlights of this Course

This graduate level course on Nonlinear Dynamics features lecture notesproblem setsexams, and related resources.

Course Description

Nonlinear dynamics with applications. Intuitive approach with emphasis on geometric thinking, computational and analytical methods. Extensive use of demonstration software. Topics: Bifurcations. Phase plane. Nonlinear coupled oscillators in biology and physics. Perturbation, averaging theory. Parametric resonances, Floquet theory. Relaxation oscillations. Hysterises. Phase locking. Chaos: Lorenz model, iterated mappings, period doubling, renormalization. Fractals. Hamiltonian systems, area preserving maps; KAM theory.

Technical Requirements

MATLAB® software is required to run the .m files found on this course site.

MATLAB® is a trademark of The MathWorks, Inc.



Prof. Rodolfo R. Rosales

Course Meeting Times

Two sessions / week
1.5 hours / session




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