Skip to content
lectern.tv
Cornell MAE 5790: Nonlinear Dynamics and Chaos →0/22
1

MAE5790-1 Course introduction and overview

1:16:31
2

MAE5790-2 One dimensional Systems

1:16:44
3

MAE5790-3 Overdamped bead on a rotating hoop

1:13:12
4

MAE5790-4 Model of an insect outbreak

1:15:16
5

MAE5790-5 Two dimensional linear systems

1:15:20
6

MAE5790-6 Two dimensional nonlinear systems fixed points

1:07:17
7

MAE5790-7 Conservative Systems

1:17:13
8

MAE5790-8 Index theory and introduction to limit cycles

1:13:55
9

Lecture 9: Testing for Closed Orbits (MAE 5790)

1:16:52
10

Lecture 10: Van der Pol Oscillator (MAE 5790)

1:05:58
11

Lecture 11: Averaging Theory for Weakly Nonlinear Oscillators (MAE 5790)

1:16:08
12

Lecture 12: Bifurcations in Two-Dimensional Systems (MAE 5790)

46:54
13

Lecture 13: Hopf Bifurcations in Aeroelastic Instabilities and Chemical Oscillators (MAE 5790)

1:07:57
14

Lecture 14: Global Bifurcations of Cycles (MAE 5790)

1:16:23
15

Lecture 15: Chaotic Waterwheel (MAE 5790)

1:14:12
16

Lecture 16: Waterwheel Equations and Lorenz Equations (MAE 5790)

1:12:42
17

Lecture 17: Chaos in the Lorenz Equations (MAE 5790)

1:16:36
18

Lecture 18: Strange Attractor for the Lorenz Equations (MAE 5790)

1:13:48
19

Lecture 19: One-Dimensional Maps (MAE 5790)

1:14:35
20

Lecture 20: Universal Aspects of Period Doubling (MAE 5790)

1:11:56
21

Lecture 21: Feigenbaum's Renormalization Analysis of Period Doubling (MAE 5790)

1:15:59
22

Lecture 22: Renormalization: Function Space and a Hands-On Calculation (MAE 5790)

1:08:32

MAE5790-1 Course introduction and overview

Steven StrogatzCornell University

Jacob Gould Schurman Professor of Applied Mathematics

1:16:31·2014·undergraduate level

This introductory lecture to Cornell MAE 5790 provides an overview of nonlinear dynamics, contrasting linear and nonlinear systems. It introduces one-dimensional systems, fixed points, and their stability, using the logistic equation as a primary example.

MathematicsEngineeringControl & Dynamical SystemsNonlinear SystemsFixed PointsLogistic Equation

Historical and logical overview of nonlinear dynamics. The structure of the course: work our way up from one to two to three-dimensional systems. Simple examples of linear vs. nonlinear systems. 1-D systems. Why pictures are more powerful than formulas for analyzing nonlinear systems. Fixed points. Stable and unstable fixed points. Example: Logistic equation in population biology.

Reading: Strogatz, "Nonlinear Dynamics and Chaos", Chapter 1 and Section 2.0--2.3.

Next · Lecture 2

MAE5790-2 One dimensional Systems

Seminar notes & discussion

Sign in to comment

No public seminar notes on this lecture yet.