18.385 Nonlinear Dynamics and Chaos, Fall 2002

18.385 Nonlinear Dynamics and Chaos, Fall 2002

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. Parame...

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Bibliographic Details
Main Author: Rosales, Rodolfo
Other Authors: Massachusetts Institute of Technology. Department of Mathematics
Format: Learning Object
Language:en-US
Published: 2002
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
Online Access:http://hdl.handle.net/1721.1/36890
Description
Summary: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.

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