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Modeling Scenario

3-004-VanderPol-ModelingScenario

Author(s): Mark Lau Kwan

University of Turabo, Gurabo PUERTO RICO

Keywords: phase plane Van der Pol oscillator limit cycle Runge-Kutta method Lienard equation

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Abstract

Resource Image This paper presents an electronic spreadsheet model of the Van der Pol oscillator, a well-known nonlinear second-order ordinary differential equation.

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Article Context

Description

The spreadsheet features a number of dynamic controls that permit the user to alter the parameters of the Van der Pol equation and explore the effects of such changes on the solution.

Furthermore, the spreadsheet exploits its graphics capabilities to produce a rendition of the limit cycle associated with the (periodic) steady-state solution to this nonlinear equation.

The Van der Pol equation models many phenomena in which periodic behavior occurs such as the oscillations encountered in electronic circuits and biological systems.

After investigating the behavior of the Van der Pol oscillator with the accompanying spreadsheet, the reader will have gained a better appreciation of limit cycles and nonlinear dynamics.

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Authors

Author(s): Mark Lau Kwan

University of Turabo, Gurabo PUERTO RICO

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