Nonlinear Dynamics and Chaos with Steven Strogatz

Course Description

This course of 25 lectures, filmed at Cornell University in Spring 2014, is intended for newcomers to nonlinear dynamics and chaos. 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.

A unique feature of the course is its emphasis on applications. These include airplane wing vibrations, biological rhythms, insect outbreaks, chemical oscillators, chaotic waterwheels, and even a technique for using chaos to send secret messages. In each case, the scientific background is explained at an elementary level and closely integrated with the mathematical theory. The theoretical work is enlivened by frequent use of computer graphics, simulations, and videotaped demonstrations of nonlinear phenomena.

The essential prerequisite is single-variable calculus, including curve sketching, Taylor series, and separable differential equations. In a few places, multivariable calculus (partial derivatives, Jacobian matrix, divergence theorem) and linear algebra (eigenvalues and eigenvectors) are used. Fourier analysis is not assumed, and is developed where needed. Introductory physics is used throughout. Other scientific prerequisites would depend on the applications considered, but in all cases, a first course should be adequate preparation.

Nonlinear Dynamics and Chaos with Steven Strogatz
The textbook written by Prof. Strogatz used for this course
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Video Lectures & Study Materials

# Lecture Play Lecture
1 Course Introduction and Overview (1:16:32) Play Video
2 One Dimensional Systems (1:16:44) Play Video
3 Overdamped Bead on a Rotating Hoop (1:13:13) Play Video
4 Model of an Insect Outbreak (1:15:16) Play Video
5 Two Dimensional Linear Systems (1:15:20) Play Video
6 Two Dimensional Nonlinear Systems: Fixed Points (1:07:17) Play Video
7 Conservative Systems (1:17:13) Play Video
8 Index Theory and Introduction to Limit Cycles (1:13:56) Play Video
9 Testing for Closed Orbits (1:16:52) Play Video
10 Van der Pol Oscillator (1:05:58) Play Video
11 Averaging Theory for Weakly Nonlinear Oscillators (1:16:08) Play Video
12 Bifurcations in Two Dimensional Systems (46:54) Play Video
13 Hopf Bifurcations in Aeroelastic Instabilities and Chemical Oscillators (1:07:57) Play Video
14 Global Bifurcations of Cycles (1:16:23) Play Video
15 Chaotic Waterwheel (1:14:12) Play Video
16 Waterwheel Equations and Lorenz Equations (1:12:42) Play Video
17 Chaos in the Lorenz Equations (1:16:36) Play Video
18 Strange Attractor for the Lorenz Equations (1:13:48) Play Video
19 One Dimensional Maps (1:14:35) Play Video
20 Universal Aspects of Period Doubling (1:11:56) Play Video
21 Feigenbaum's Renormalization Analysis of Period Doubling (1:15:59) Play Video
22 Renormalization: Function Space and a Hands-on Calculation (1:08:33) Play Video
23 Fractals and the Geometry of Strange Attractors (1:04:33) Play Video
24 Hénon Map (51:24) Play Video
25 Using Chaos to Send Secret Messages (1:05:22) Play Video


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