Oscillations in a Slow-Fast Paleoclimate Model for Glacial Cycles
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912546429075456 |
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| author | García-Rivera, Marco Polo Álvarez-Ramírez, Martha Jardón-Kojakhmetov, Hildeberto |
| author_facet | García-Rivera, Marco Polo Álvarez-Ramírez, Martha Jardón-Kojakhmetov, Hildeberto |
| contents | This paper investigates a deterministic variant of the Saltzman-Maasch model for Pleistocene glacial cycles, formulated as a three-dimensional dynamical system with cubic feedback in the atmospheric carbon dioxide equation. After reducing the model to a planar system on a critical manifold, we perform a detailed bifurcation analysis and identify both Hopf and Bautin (generalized Hopf) bifurcations, which govern the emergence of stable and unstable limit cycles. To analyze global transitions, we perform a rescaling of time and variables to derive a leading-order Hamiltonian system. This reduction enables the explicit construction of homoclinic orbits and the application of Melnikov's method to assess their persistence under perturbations. The analytical findings are further corroborated by numerical simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_15206 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Oscillations in a Slow-Fast Paleoclimate Model for Glacial Cycles García-Rivera, Marco Polo Álvarez-Ramírez, Martha Jardón-Kojakhmetov, Hildeberto Dynamical Systems Classical Analysis and ODEs Chaotic Dynamics 86A40(Primary) 37N10 (Secondary) This paper investigates a deterministic variant of the Saltzman-Maasch model for Pleistocene glacial cycles, formulated as a three-dimensional dynamical system with cubic feedback in the atmospheric carbon dioxide equation. After reducing the model to a planar system on a critical manifold, we perform a detailed bifurcation analysis and identify both Hopf and Bautin (generalized Hopf) bifurcations, which govern the emergence of stable and unstable limit cycles. To analyze global transitions, we perform a rescaling of time and variables to derive a leading-order Hamiltonian system. This reduction enables the explicit construction of homoclinic orbits and the application of Melnikov's method to assess their persistence under perturbations. The analytical findings are further corroborated by numerical simulations. |
| title | Oscillations in a Slow-Fast Paleoclimate Model for Glacial Cycles |
| topic | Dynamical Systems Classical Analysis and ODEs Chaotic Dynamics 86A40(Primary) 37N10 (Secondary) |
| url | https://arxiv.org/abs/2508.15206 |