MAE 5790: Nonlinear Dynamics and Chaos
MAE 5790: Nonlinear Dynamics and Chaos (Spring 2014, Cornell University). Instructor: Professor Steven Strogatz. This course provides an introduction to nonlinear dynamics, with applications to physics, engineering, biology, and chemistry. It closely follows Prof. Strogatz's book, "Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering."
The mathematical treatment is friendly and informal, but still careful. Analytical methods, concrete examples, and geometric intuition are stressed. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.
| Lecture 19 - One Dimensional Maps |
Logistic map: a simple mathematical model with very complicated dynamics. Influential article by Robert May. Numerical results: Fixed points. Cycles of period 2, 4, 8, 16, .... The period-doubling route to chaos. An icon of chaos: The orbit diagram. Chaos intermingled with periodic windows. Period-3 window. Analytical results: Fixed points and their stability. Flip bifurcation (eigenvalue = -1) at period doubling. Period-2 points and their stability.
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