18.385 Nonlinear Dynamics and Chaos, Fall 2002

Rosales, Rodolfo

Author(s)

Rosales, Rodolfo

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Alternative title

Nonlinear Dynamics and Chaos

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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.

Date issued

2002-12

URI

http://hdl.handle.net/1721.1/36890

Department

Massachusetts Institute of Technology. Department of Mathematics

Other identifiers

18.385-Fall2002

local: 18.385

local: IMSCP-MD5-5fd714015fd58337b1dbcc699ddd8658

Keywords

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

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