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On the numerical continuation of isolas of equilibria

Rodrigues, S.; Desroches, M.; Avitabile, D.

Authors

S. Rodrigues

M. Desroches

D. Avitabile



Abstract

We present a numerical strategy to compute one-parameter families of isolas of equilibrium solutions in ODEs. Isolas are solution branches closed in parameter space. Numerical continuation is required to compute one single isola since it contains at least one unstable segment. We show how to use pseudo-arclength predictor-corrector schemes in order to follow an entire isola in parameter space, as an individual object, by posing a suitable algebraic problem. We continue isolas of equilibria in a two-dimensional dynamical system, the so-called continuous stirred tank reactor model, and also in a three-dimensional model related to plasma physics. We then construct a toy model and follow a family of isolas past a fold and illustrate how to initiate the computation close to a formation center, using approximate ellipses in a model inspired by the Van der Pol equation. We also show how to introduce node adaptivity in the discretization of the isola, so as to concentrate nodes in region with higher curvature. We conclude by commenting on the extension of the proposed numerical strategy to the case of isolas of periodic orbits.

Citation

RODRIGUES, S., DESROCHES, M., AVITABILE, D., Desroches, M., & Rodrigues, S. (2012). On the numerical continuation of isolas of equilibria. International Journal of Bifurcation and Chaos, 22(11), 1250277. https://doi.org/10.1142/s021812741250277x

Journal Article Type Article
Online Publication Date Apr 12, 2012
Publication Date 2012-11
Deposit Date Feb 27, 2013
Publicly Available Date Feb 27, 2013
Journal International Journal of Bifurcation and Chaos
Print ISSN 0218-1274
Electronic ISSN 1793-6551
Publisher World Scientific
Peer Reviewed Peer Reviewed
Volume 22
Issue 11
Article Number 1250277
Pages 1250277
DOI https://doi.org/10.1142/s021812741250277x
Keywords Modelling and Simulation; Applied Mathematics
Public URL http://eprints.nottingham.ac.uk/id/eprint/1652
Publisher URL http://www.worldscientific.com/doi/abs/10.1142/S021812741250277X
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf
Additional Information Electronic version of an article published as International Journal of Bifurcation and Chaos, 22, 11, 2012, 1250277, doi: 10.1142/S021812741250277X © World Scientific Publishing Company, http://www.worldscientific.com/doi/abs/10.1142/S021812741250277X

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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