A degenerate Takens--Bogdanov bifurcation in a normal form of Lorenz's equations
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916660796981248 |
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| author | Algaba, A. Domínguez-Moreno, M. C. Merino, M. Rodríguez-Luis, A. J. |
| author_facet | Algaba, A. Domínguez-Moreno, M. C. Merino, M. Rodríguez-Luis, A. J. |
| contents | In this work we consider an unfolding of a normal form of the Lorenz system near a triple-zero singularity. We are interested in the analysis of double-zero bifurcations emerging from that singularity. Their local study provide partial results that are extended by means of numerical continuation methods. Specifically, a curve of heteroclinic connections is detected. It has a degenerate point from which infinitely many homoclinic connections emerge. In this way, we can partially understand the dynamics near the triple-zero singularity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_18662 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A degenerate Takens--Bogdanov bifurcation in a normal form of Lorenz's equations Algaba, A. Domínguez-Moreno, M. C. Merino, M. Rodríguez-Luis, A. J. Dynamical Systems Chaotic Dynamics 37G10 In this work we consider an unfolding of a normal form of the Lorenz system near a triple-zero singularity. We are interested in the analysis of double-zero bifurcations emerging from that singularity. Their local study provide partial results that are extended by means of numerical continuation methods. Specifically, a curve of heteroclinic connections is detected. It has a degenerate point from which infinitely many homoclinic connections emerge. In this way, we can partially understand the dynamics near the triple-zero singularity. |
| title | A degenerate Takens--Bogdanov bifurcation in a normal form of Lorenz's equations |
| topic | Dynamical Systems Chaotic Dynamics 37G10 |
| url | https://arxiv.org/abs/2503.18662 |