Asymptotic limits of the principal spectrum point of a nonlocal dispersal cooperative system and application to a two-stage structured population model
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2023
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| author | Onyido, Maria A. Salako, Rachidi B. Uba, Markjoe O. Udeani, Cyril I. |
| author_facet | Onyido, Maria A. Salako, Rachidi B. Uba, Markjoe O. Udeani, Cyril I. |
| contents | This work examines the limits of the principal spectrum point, $λ_p$, of a nonlocal dispersal cooperative system with respect to the dispersal rates. In particular, we provide precise information on the sign of $λ_p$ as one of the dispersal rates is : (i) small while the other dispersal rate is arbitrary, and (ii) large while the other is either also large or fixed. We then apply our results to study the effects of dispersal rates on a two-stage structured nonlocal dispersal population model whose linearized system at the trivial solution results in a nonlocal dispersal cooperative system. The asymptotic profiles of the steady-state solutions with respect to the dispersal rates of the two-stage nonlocal dispersal population model are also obtained. Some biological interpretations of our results are discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_17734 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Asymptotic limits of the principal spectrum point of a nonlocal dispersal cooperative system and application to a two-stage structured population model Onyido, Maria A. Salako, Rachidi B. Uba, Markjoe O. Udeani, Cyril I. Analysis of PDEs Dynamical Systems 92D40, 92D50, 35P15, 35K57 This work examines the limits of the principal spectrum point, $λ_p$, of a nonlocal dispersal cooperative system with respect to the dispersal rates. In particular, we provide precise information on the sign of $λ_p$ as one of the dispersal rates is : (i) small while the other dispersal rate is arbitrary, and (ii) large while the other is either also large or fixed. We then apply our results to study the effects of dispersal rates on a two-stage structured nonlocal dispersal population model whose linearized system at the trivial solution results in a nonlocal dispersal cooperative system. The asymptotic profiles of the steady-state solutions with respect to the dispersal rates of the two-stage nonlocal dispersal population model are also obtained. Some biological interpretations of our results are discussed. |
| title | Asymptotic limits of the principal spectrum point of a nonlocal dispersal cooperative system and application to a two-stage structured population model |
| topic | Analysis of PDEs Dynamical Systems 92D40, 92D50, 35P15, 35K57 |
| url | https://arxiv.org/abs/2306.17734 |