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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)

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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)

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

1:08:32

Lecture 10: Van der Pol Oscillator (MAE 5790)

Steven StrogatzCornell University

Professor

1:05:58·2014·undergraduate level

This session investigates the van der Pol oscillator, tracing its origins in radio engineering and analyzing both its strongly and weakly nonlinear limits. It covers the Liénard transformation, relaxation oscillations, and the energy method for estimating limit cycle amplitude.

MathematicsEngineeringControl & Dynamical SystemsVan der Pol OscillatorRelaxation OscillationsLiénard Transformation

Origins of the van der Pol oscillator in radio engineering. Strongly nonlinear limit. Liénard transformation. Relaxation oscillations. Weakly nonlinear limit. Energy method for estimating the amplitude of the limit cycle.

Reading: Strogatz, "Nonlinear Dynamics and Chaos", Sections 7.4--7.6.

Previous · Lecture 9

Lecture 9: Testing for Closed Orbits (MAE 5790)

Next · Lecture 11

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

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