Steady-state dynamics in a two-patch population model with and without Allee effect
Most biological populations reside in landscapes that consist of many different patches of different quality. Different species differ in their movement behavior, habitat preference and growth rates. Historically, mathematical models for population dynamics have made many simplifying assumptions, su...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Western Libraries
2023-09-01
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| Series: | Mathematics in Applied Sciences and Engineering |
| Subjects: | |
| Online Access: | https://ojs.lib.uwo.ca/index.php/mase/article/view/16474 |
| _version_ | 1797662219415060480 |
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| author | Laurence Ketchemen Tchouaga Frithjof Lutscher |
| author_facet | Laurence Ketchemen Tchouaga Frithjof Lutscher |
| author_sort | Laurence Ketchemen Tchouaga |
| collection | DOAJ |
| description | Most biological populations reside in landscapes that consist of many different patches of different quality. Different species differ in their movement behavior, habitat preference and growth rates. Historically, mathematical models for population dynamics have made many simplifying assumptions, such as a single patch or homogeneous landscapes. Recent models have begun to implement landscape heterogeneity and individual movement characteristics, but many of those are based on logistic growth and linear analysis of the zero state. We consider a two-patch model with more general growth functions that can include Allee effects. We prove the existence of steady states and classify their qualitative behavior. In some special cases, we explicitly calculate their stability and use these results to give conditions for when the system exhibits bistability, i.e., the coexistence of locally stable states. We also study bifurcations with respect to the size of habitat patches and give conditions for forward and backward bifurcations. |
| first_indexed | 2024-03-11T18:56:58Z |
| format | Article |
| id | doaj.art-de1c318b046a4880ae96953e56212405 |
| institution | Directory Open Access Journal |
| issn | 2563-1926 |
| language | English |
| last_indexed | 2024-03-11T18:56:58Z |
| publishDate | 2023-09-01 |
| publisher | Western Libraries |
| record_format | Article |
| series | Mathematics in Applied Sciences and Engineering |
| spelling | doaj.art-de1c318b046a4880ae96953e562124052023-10-10T21:01:58ZengWestern LibrariesMathematics in Applied Sciences and Engineering2563-19262023-09-014319622610.5206/mase/1647410728Steady-state dynamics in a two-patch population model with and without Allee effectLaurence Ketchemen TchouagaFrithjof LutscherMost biological populations reside in landscapes that consist of many different patches of different quality. Different species differ in their movement behavior, habitat preference and growth rates. Historically, mathematical models for population dynamics have made many simplifying assumptions, such as a single patch or homogeneous landscapes. Recent models have begun to implement landscape heterogeneity and individual movement characteristics, but many of those are based on logistic growth and linear analysis of the zero state. We consider a two-patch model with more general growth functions that can include Allee effects. We prove the existence of steady states and classify their qualitative behavior. In some special cases, we explicitly calculate their stability and use these results to give conditions for when the system exhibits bistability, i.e., the coexistence of locally stable states. We also study bifurcations with respect to the size of habitat patches and give conditions for forward and backward bifurcations.https://ojs.lib.uwo.ca/index.php/mase/article/view/16474reaction–diffusion systeminterface conditionssteady statepopulation dynamicsalee effectbifurcation. |
| spellingShingle | Laurence Ketchemen Tchouaga Frithjof Lutscher Steady-state dynamics in a two-patch population model with and without Allee effect Mathematics in Applied Sciences and Engineering reaction–diffusion system interface conditions steady state population dynamics alee effect bifurcation. |
| title | Steady-state dynamics in a two-patch population model with and without Allee effect |
| title_full | Steady-state dynamics in a two-patch population model with and without Allee effect |
| title_fullStr | Steady-state dynamics in a two-patch population model with and without Allee effect |
| title_full_unstemmed | Steady-state dynamics in a two-patch population model with and without Allee effect |
| title_short | Steady-state dynamics in a two-patch population model with and without Allee effect |
| title_sort | steady state dynamics in a two patch population model with and without allee effect |
| topic | reaction–diffusion system interface conditions steady state population dynamics alee effect bifurcation. |
| url | https://ojs.lib.uwo.ca/index.php/mase/article/view/16474 |
| work_keys_str_mv | AT laurenceketchementchouaga steadystatedynamicsinatwopatchpopulationmodelwithandwithoutalleeeffect AT frithjoflutscher steadystatedynamicsinatwopatchpopulationmodelwithandwithoutalleeeffect |