Bifurcations of the Hénon map with additive bounded noise
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918413674217472 |
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| author | Lamb, Jeroen S. W. Rasmussen, Martin Tey, Wei Hao |
| author_facet | Lamb, Jeroen S. W. Rasmussen, Martin Tey, Wei Hao |
| contents | We numerically study bifurcations of attractors of the Hénon map with additive bounded noise with spherical reach. The bifurcations are analysed using a finite-dimensional boundary map. We distinguish between two types of bifurcations: topological bifurcations and boundary bifurcations. Topological bifurcations describe discontinuous changes of attractors and boundary bifurcations occur when singularities of an attractor's boundary are created or destroyed. We identify correspondences between topological and boundary bifurcations of attractors and local and global bifurcations of the boundary map. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_02776 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bifurcations of the Hénon map with additive bounded noise Lamb, Jeroen S. W. Rasmussen, Martin Tey, Wei Hao Dynamical Systems Optimization and Control 37C70, 37B25, 37H20 We numerically study bifurcations of attractors of the Hénon map with additive bounded noise with spherical reach. The bifurcations are analysed using a finite-dimensional boundary map. We distinguish between two types of bifurcations: topological bifurcations and boundary bifurcations. Topological bifurcations describe discontinuous changes of attractors and boundary bifurcations occur when singularities of an attractor's boundary are created or destroyed. We identify correspondences between topological and boundary bifurcations of attractors and local and global bifurcations of the boundary map. |
| title | Bifurcations of the Hénon map with additive bounded noise |
| topic | Dynamical Systems Optimization and Control 37C70, 37B25, 37H20 |
| url | https://arxiv.org/abs/2504.02776 |