On the numerical continuation of isolas of equilibria

Avitabile, Daniele and Desroches, Mathieu and Rodrigues, Serafim (2012) On the numerical continuation of isolas of equilibria. International Journal of Bifurcation and Chaos, 22 (11). 1250277/1- 1250277/12. ISSN 0218-1274 (In Press)

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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.

Item Type: Article
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
Schools/Departments: University of Nottingham UK Campus > Faculty of Science > School of Mathematical Sciences
Depositing User: Avitabile, Dr. Daniele
Date Deposited: 27 Feb 2013 10:08
Last Modified: 11 May 2016 16:46
URI: http://eprints.nottingham.ac.uk/id/eprint/1652

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