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Your search keyword '"van den Berg, Jan"' showing total 5 results
Start Over Author "van den Berg, Jan" Topic computer-assisted proofs
5 results on '"van den Berg, Jan"'

4. Rigorous Verification of Hopf Bifurcations via Desingularization and Continuation.

Author

van den Berg, Jan Bouwe, Lessard, Jean-Philippe, and Queirolo, Elena

Subjects
*HOPF bifurcations, *CONTINUATION methods
Abstract

In this paper we present a general approach to rigorously validate Hopf bifurcations as well as saddle-node bifurcations of periodic orbits in systems of ODEs. By a combination of analytic estimates and computer-assisted calculations, we follow solution curves of cycles through folds, checking along the way that a single nondegenerate saddle-node bifurcation occurs. Similarly, we rigorously continue solution curves of cycles starting from their onset at a Hopf bifurcation. We use a blowup analysis to regularize the continuation problem near the Hopf bifurcation point. This extends the applicability of validated continuation methods to the mathematically rigorous computational study of bifurcation problems. [ABSTRACT FROM AUTHOR]

Published
2021
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5. Validated Chebyshev-based Computations for Ordinary and Partial Differential Equations

Author

Sheombarsing, R.S.S., van den Berg, Jan Bouwe, Rink, Bob, and Mathematics

Subjects
Differential equations, heteroclinic orbits, Validated computations, Chebyshev interpolation, Chebyshev series, periodic orbits, unstable manifold, parabolic PDE, Dynamical systems, connecting orbits, Computer-assisted proofs, nonlinear dynamics, stable manifold
Published
2018

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