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- W4287753422 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." @default.
- W4287753422 created "2022-07-26" @default.
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- W4287753422 date "2020-06-23" @default.
- W4287753422 modified "2023-09-29" @default.
- W4287753422 title "Rigorous verification of Hopf bifurcations via desingularization and continuation" @default.
- W4287753422 doi "https://doi.org/10.48550/arxiv.2006.13373" @default.
- W4287753422 hasPublicationYear "2020" @default.
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