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Cornell MAE 5790: Nonlinear Dynamics and Chaos →0/22
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MAE5790-1 Course introduction and overview

1:16:31
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MAE5790-2 One dimensional Systems

1:16:44
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MAE5790-3 Overdamped bead on a rotating hoop

1:13:12
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MAE5790-4 Model of an insect outbreak

1:15:16
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MAE5790-5 Two dimensional linear systems

1:15:20
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MAE5790-6 Two dimensional nonlinear systems fixed points

1:07:17
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MAE5790-7 Conservative Systems

1:17:13
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MAE5790-8 Index theory and introduction to limit cycles

1:13:55
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Testing for Closed Orbits

1:16:52
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Van der Pol Oscillator

1:05:58
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Averaging Theory for Weakly Nonlinear Oscillators

1:16:08
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Bifurcations in Two-Dimensional Systems

46:54
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Hopf Bifurcations in Aeroelastic Instabilities and Chemical Oscillators

1:07:57
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Global Bifurcations of Cycles

1:16:23
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Chaotic Waterwheel

1:14:12
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Waterwheel Equations and Lorenz Equations

1:12:42
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Chaos in the Lorenz Equations

1:16:36
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Strange Attractor for the Lorenz Equations

1:13:48
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One-Dimensional Maps

1:14:35
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Universal Aspects of Period Doubling

1:11:56
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Feigenbaum's Renormalization Analysis of Period Doubling

1:15:59
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Renormalization: Function Space and a Hands-On Calculation

1:08:32

Chaos in the Lorenz Equations

Steven StrogatzDistinguishedCornell University

Professor

1:16:36·2014·undergraduate level

This lecture delves into the chaotic behavior of the Lorenz equations, discussing global stability, boundedness, and the absence of quasiperiodicity. It introduces the strange attractor, butterfly effect, and Lyapunov exponent, defining the predictability horizon for chaotic systems.

MathematicsEngineeringControl & Dynamical SystemsLorenz SystemChaosStrange Attractor

Global stability for the origin for r is less than 1. Liapunov 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. Liapunov exponent. Predictability horizon for the weather and solar system. Formula for the predictability horizon (Liapunov time), based on rate of separation of nearby trajectories. What is meant by saying that chaotic systems are unpredictable?

Reading: Strogatz, "Nonlinear Dynamics and Chaos", Sections 9.2, 9.3.

LecturerAll lecturers →
Steven StrogatzDistinguished

Winthrop Professor of Applied Mathematics, Cornell University

Cornell mathematician renowned for nonlinear dynamics, chaos theory, small-world networks, and mathematical exposition.

2 courses · 43 lecturesCanon
Previous · Lecture 16

Waterwheel Equations and Lorenz Equations

Next · Lecture 18

Strange Attractor for the Lorenz Equations

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