18.385 Nonlinear Dynamics and Chaos, Fall 2002

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Author(s)
Rosales, Rodolfo
Alternative Title
Nonlinear Dynamics and Chaos
Date Issued
December 2002
Abstract
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.
Subjects
Phase plane
limit cycles
Poincare-Bendixson theory
Time-dependent systems
Floquet theory
Poincare maps
averaging
Stability of equilibria
near-equilibrium dynamics
Center manifolds
elementary bifurcations
normal forms
chaos
Chaotic behavior in systems
Dynamics
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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