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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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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)

1:16:23
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Lecture 15: Chaotic Waterwheel (MAE 5790)

1:14:12
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Lecture 16: Waterwheel Equations and Lorenz Equations (MAE 5790)

1:12:42
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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)

1:13:48
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Lecture 19: One-Dimensional Maps (MAE 5790)

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

1:11:56
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Lecture 21: Feigenbaum's Renormalization Analysis of Period Doubling (MAE 5790)

1:15:59
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Lecture 22: Renormalization: Function Space and a Hands-On Calculation (MAE 5790)

1:08:32

Lecture 9: Testing for Closed Orbits (MAE 5790)

Steven StrogatzCornell University

Professor

1:16:52·2014·undergraduate level

This lecture explores techniques for discerning and proving the existence of closed orbits, examining index theory, Dulac's criterion, and the Poincaré-Bendixson theorem. It illustrates these concepts with examples like oscillatory glycolysis and trapping regions.

MathematicsEngineeringControl & Dynamical SystemsIndex TheoryDulac's CriterionPoincaré-Bendixson Theorem

Techniques for ruling out closed orbits: index theory and Dulac's criterion. Techniques for proving closed orbits exist: Poincaré-Bendixson theorem. Trapping regions. Example in polar coordinates. Simple model of oscillatory glycolysis in metabolism. Nullclines.

Reading: Strogatz, "Nonlinear Dynamics and Chaos", Sections 7.2, 7.3.

Previous · Lecture 8

MAE5790-8 Index theory and introduction to limit cycles

Next · Lecture 10

Lecture 10: Van der Pol Oscillator (MAE 5790)

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