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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

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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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Lecture 9: Testing for Closed Orbits (MAE 5790)

1:16:52
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Lecture 10: Van der Pol Oscillator (MAE 5790)

1:05:58
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Lecture 11: Averaging Theory for Weakly Nonlinear Oscillators (MAE 5790)

1:16:08
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Lecture 12: Bifurcations in Two-Dimensional Systems (MAE 5790)

46:54
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Lecture 13: Hopf Bifurcations in Aeroelastic Instabilities and Chemical Oscillators (MAE 5790)

1:07:57
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Lecture 14: Global Bifurcations of Cycles (MAE 5790)

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Lecture 15: Chaotic Waterwheel (MAE 5790)

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

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

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

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Lecture 19: One-Dimensional Maps (MAE 5790)

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

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

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

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Lecture 19: One-Dimensional Maps (MAE 5790)

Steven StrogatzCornell University

Professor

1:14:35·2014·undergraduate level

This lecture examines one-dimensional maps, focusing on the logistic map as a model for complex dynamics and the period-doubling route to chaos. It analyzes fixed points, their stability, and the iconic orbit diagram, including flip bifurcations.

MathematicsEngineeringControl & Dynamical SystemsLinear AlgebraOne-Dimensional MapsLogistic Map

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.

Reading: Strogatz, "Nonlinear Dynamics and Chaos", Sections 10.0-10.2.

Previous · Lecture 18

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

Next · Lecture 20

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

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