Spatially inhomogeneous two-cycles in an integrodifference equation
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908609536851968 |
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| author | Church, Kevin Constantineau, Kevin Lessard, Jean-Philippe |
| author_facet | Church, Kevin Constantineau, Kevin Lessard, Jean-Philippe |
| contents | In this work, we prove the existence of a 2-cycle in an integrodifference equation with a Laplace kernel and logistic growth function, connecting two non-trivial fixed points of the second iterate of the logistic map in the non-chaotic regime. This model was first studied by Kot (1992), and the 2-cycle we establish corresponds to one numerically observed by Bourgeois, Leblanc, and Lutscher (2018) for the Ricker growth function. We provide strong evidence that the 2-cycle for the Ricker growth function can be rigorously proven using a similar approach. Finally, we present numerical results indicating that both 2-cycles exhibit spectral stability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_21134 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spatially inhomogeneous two-cycles in an integrodifference equation Church, Kevin Constantineau, Kevin Lessard, Jean-Philippe Dynamical Systems Functional Analysis Populations and Evolution In this work, we prove the existence of a 2-cycle in an integrodifference equation with a Laplace kernel and logistic growth function, connecting two non-trivial fixed points of the second iterate of the logistic map in the non-chaotic regime. This model was first studied by Kot (1992), and the 2-cycle we establish corresponds to one numerically observed by Bourgeois, Leblanc, and Lutscher (2018) for the Ricker growth function. We provide strong evidence that the 2-cycle for the Ricker growth function can be rigorously proven using a similar approach. Finally, we present numerical results indicating that both 2-cycles exhibit spectral stability. |
| title | Spatially inhomogeneous two-cycles in an integrodifference equation |
| topic | Dynamical Systems Functional Analysis Populations and Evolution |
| url | https://arxiv.org/abs/2510.21134 |