Analysis of a May-Holling-Tanner ratio-dependent predator-prey model with an alternative food source for the predator and a strong Allee effect for the prey
This paper presents a detailed analysis of a bitrophic chain to understand the complex ecological behaviour applied to this specific model. The model is described by means of a two-dimensional system of ordinary differential equations. The existence and uniqueness of the solutions of this system ar...
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| Format: | Article |
| Language: | English |
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Western Libraries
2024-12-01
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| Series: | Mathematics in Applied Sciences and Engineering |
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| Online Access: | https://ojs.lib.uwo.ca/index.php/mase/article/view/19417 |
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| author | Marco-Antonio Romero-Ordoñez Jhelly-Reynaluz Pérez-Núñez Neisser Pino-Romero |
| author_facet | Marco-Antonio Romero-Ordoñez Jhelly-Reynaluz Pérez-Núñez Neisser Pino-Romero |
| author_sort | Marco-Antonio Romero-Ordoñez |
| collection | DOAJ |
| description |
This paper presents a detailed analysis of a bitrophic chain to understand the complex ecological behaviour applied to this specific model. The model is described by means of a two-dimensional system of ordinary differential equations. The existence and uniqueness of the solutions of this system are examined, as well as their boundedness and positivity. In addition, through a differentiable equivalence, conditions for local and global stability at biologically relevant critical points are established. Periodic solutions are also explored. Finally, the Python programming language is used to perform a quantitative analysis of these critical points, showing different scenarios of the qualitative analysis previously obtained.
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| format | Article |
| id | doaj-art-760b634266864b499b36da1125f0d35e |
| institution | Kabale University |
| issn | 2563-1926 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Western Libraries |
| record_format | Article |
| series | Mathematics in Applied Sciences and Engineering |
| spelling | doaj-art-760b634266864b499b36da1125f0d35e2025-01-03T18:35:34ZengWestern LibrariesMathematics in Applied Sciences and Engineering2563-19262024-12-015410.5206/mase/19417Analysis of a May-Holling-Tanner ratio-dependent predator-prey model with an alternative food source for the predator and a strong Allee effect for the preyMarco-Antonio Romero-Ordoñezhttps://orcid.org/0000-0002-7383-4837Jhelly-Reynaluz Pérez-Núñezhttps://orcid.org/0000-0003-0717-8277Neisser Pino-Romerohttps://orcid.org/0000-0002-9865-5974 This paper presents a detailed analysis of a bitrophic chain to understand the complex ecological behaviour applied to this specific model. The model is described by means of a two-dimensional system of ordinary differential equations. The existence and uniqueness of the solutions of this system are examined, as well as their boundedness and positivity. In addition, through a differentiable equivalence, conditions for local and global stability at biologically relevant critical points are established. Periodic solutions are also explored. Finally, the Python programming language is used to perform a quantitative analysis of these critical points, showing different scenarios of the qualitative analysis previously obtained. https://ojs.lib.uwo.ca/index.php/mase/article/view/19417Strong Allee effect, alternative food, differential equations, Liapunov function, Chetaev criterion. |
| spellingShingle | Marco-Antonio Romero-Ordoñez Jhelly-Reynaluz Pérez-Núñez Neisser Pino-Romero Analysis of a May-Holling-Tanner ratio-dependent predator-prey model with an alternative food source for the predator and a strong Allee effect for the prey Mathematics in Applied Sciences and Engineering Strong Allee effect, alternative food, differential equations, Liapunov function, Chetaev criterion. |
| title | Analysis of a May-Holling-Tanner ratio-dependent predator-prey model with an alternative food source for the predator and a strong Allee effect for the prey |
| title_full | Analysis of a May-Holling-Tanner ratio-dependent predator-prey model with an alternative food source for the predator and a strong Allee effect for the prey |
| title_fullStr | Analysis of a May-Holling-Tanner ratio-dependent predator-prey model with an alternative food source for the predator and a strong Allee effect for the prey |
| title_full_unstemmed | Analysis of a May-Holling-Tanner ratio-dependent predator-prey model with an alternative food source for the predator and a strong Allee effect for the prey |
| title_short | Analysis of a May-Holling-Tanner ratio-dependent predator-prey model with an alternative food source for the predator and a strong Allee effect for the prey |
| title_sort | analysis of a may holling tanner ratio dependent predator prey model with an alternative food source for the predator and a strong allee effect for the prey |
| topic | Strong Allee effect, alternative food, differential equations, Liapunov function, Chetaev criterion. |
| url | https://ojs.lib.uwo.ca/index.php/mase/article/view/19417 |
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