A density-dependent metapopulation model: Extinction, persistence and source-sink dynamics
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911870040932352 |
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| author | McGrane-Corrigan, Blake Mason, Oliver Moral, Rafael de Andrade |
| author_facet | McGrane-Corrigan, Blake Mason, Oliver Moral, Rafael de Andrade |
| contents | We consider a nonlinear coupled discrete-time model of population dynamics. This model describes the movement of populations within a heterogeneous landscape, where the growth of subpopulations are modelled by (possibly different) bounded Kolmogorov maps and coupling terms are defined by nonlinear functions taking values in $(0,1)$. These couplings describe the proportions of individuals dispersing between regions. We first give a brief survey of similar discrete-time dispersal models. We then derive sufficient conditions for the stability/instability of the extinction equilibrium, for the existence of a positive fixed point and for ensuring uniform strong persistence. Finally we numerically explore a planar version of our model in a source-sink context, to show some of the qualitative behaviour that the model we consider can capture: for example, periodic behaviour and dynamics reminiscent of chaos. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_04505 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A density-dependent metapopulation model: Extinction, persistence and source-sink dynamics McGrane-Corrigan, Blake Mason, Oliver Moral, Rafael de Andrade Dynamical Systems 37N25 (Primary) 39A30, 92D25 (Secondary) We consider a nonlinear coupled discrete-time model of population dynamics. This model describes the movement of populations within a heterogeneous landscape, where the growth of subpopulations are modelled by (possibly different) bounded Kolmogorov maps and coupling terms are defined by nonlinear functions taking values in $(0,1)$. These couplings describe the proportions of individuals dispersing between regions. We first give a brief survey of similar discrete-time dispersal models. We then derive sufficient conditions for the stability/instability of the extinction equilibrium, for the existence of a positive fixed point and for ensuring uniform strong persistence. Finally we numerically explore a planar version of our model in a source-sink context, to show some of the qualitative behaviour that the model we consider can capture: for example, periodic behaviour and dynamics reminiscent of chaos. |
| title | A density-dependent metapopulation model: Extinction, persistence and source-sink dynamics |
| topic | Dynamical Systems 37N25 (Primary) 39A30, 92D25 (Secondary) |
| url | https://arxiv.org/abs/2405.04505 |