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 17 - Chaos in the Lorenz Equations |
Global stability for the origin for r is less than 1. Lyapunov function. Boundedness. Hopf bifurcations. No quasiperiodicity. Simulations of the Lorenz system. Stories of how Lorenz made his discovery. Strange attractor and butterfly effect. Exponential divergence of nearby trajectories. Lyapunov exponent. Predictability horizon for the weather and solar system. Formula for the predictability horizon (Lyapunov time), based on rate of separation of nearby trajectories. What is meant by saying that chaotic systems are unpredictable?
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