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Investigating Torus Bifurcations in the Forced Van Der Pol Oscillator

Krauskopf, Bernd and Osinga, Hinke M. (2000) Investigating Torus Bifurcations in the Forced Van Der Pol Oscillator. In: Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems. IMA Volumes in Mathematics and its Applications. No.119. Springer , New York, NY, pp. 199-208. ISBN 978-1-4612-7044-7. https://resolver.caltech.edu/CaltechAUTHORS:20191209-131509521

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Abstract

We demonstrate a new algorithm for computing one-dimensional stable and unstable manifolds of (Poincaré) maps that we have implemented in DsTool [1]. As an example we investigate the most complicated sequence of bifurcations in the forced Van der Pol oscillator as the amplitude of the forcing is increased. This bifurcation sequence has recently been used to test algorithms for the computation of invariant tori.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/978-1-4612-1208-9_9DOIArticle
https://rdcu.be/b32WZPublisherFree ReadCube access
Additional Information:© 2000 Springer Science+Business Media New York. We thank J. Guckenheimer, J. Lorenz and V. Reichelt for helpful discussions. B.K. thanks the Institute for Mathematics and its Applications for its hospitality and for financial support.
Funders:
Funding AgencyGrant Number
Institute for Mathematics and its ApplicationsUNSPECIFIED
Subject Keywords:Numerical computations of (un)stable manifolds; Poincaré map; invariant torus; Van der Pol oscillator
Series Name:IMA Volumes in Mathematics and its Applications
Issue or Number:119
Record Number:CaltechAUTHORS:20191209-131509521
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20191209-131509521
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:100242
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:09 Dec 2019 21:46
Last Modified:08 May 2020 21:04

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