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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.03984 |
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| _version_ | 1866913824117882880 |
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| author | de Leenheer, Patrick MacDonald, Jane Shaw Patel, Swati |
| author_facet | de Leenheer, Patrick MacDonald, Jane Shaw Patel, Swati |
| contents | We revisit a model proposed by Freedman etal in \cite{freedman} which describes the dynamics of a population diffusing in a patchy environment. From their work it is known that positive steady states exist for this model, but not whether they are unique. Here, we provide sufficient conditions guaranteeing that steady states are unique. These conditions are satisfied when the reaction rates are generalized logistic growth rates. Our proofs critically exploit Chicone's ideas in \cite{chicone}, which were used to establish that the period map associated to a continuous family of periodic solutions of certain planar Hamiltonian systems is monotone. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_03984 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unique steady states for population models in a heterogeneous environment de Leenheer, Patrick MacDonald, Jane Shaw Patel, Swati Dynamical Systems We revisit a model proposed by Freedman etal in \cite{freedman} which describes the dynamics of a population diffusing in a patchy environment. From their work it is known that positive steady states exist for this model, but not whether they are unique. Here, we provide sufficient conditions guaranteeing that steady states are unique. These conditions are satisfied when the reaction rates are generalized logistic growth rates. Our proofs critically exploit Chicone's ideas in \cite{chicone}, which were used to establish that the period map associated to a continuous family of periodic solutions of certain planar Hamiltonian systems is monotone. |
| title | Unique steady states for population models in a heterogeneous environment |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2505.03984 |