Fractional-Order Food Chain Model with Omnivore and Anti-Predator
A fractional-order food chain model is proposed in this article. The model is built by prey, intermediate predator, and omnivore. It is assumed that intermediate predator only eat prey and omnivore can consume prey and intermediate predator. But, prey has the ability called as anti-predator behavior...
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| Format: | Article |
| Language: | English |
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Indonesian Bio-Mathematical Society
2023-01-01
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| Series: | Communication in Biomathematical Sciences |
| Subjects: | |
| Online Access: | https://journals.itb.ac.id/index.php/cbms/article/view/18694 |
| _version_ | 1797244969429237760 |
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| author | Adin Lazuardy Firdiansyah |
| author_facet | Adin Lazuardy Firdiansyah |
| author_sort | Adin Lazuardy Firdiansyah |
| collection | DOAJ |
| description | A fractional-order food chain model is proposed in this article. The model is built by prey, intermediate predator, and omnivore. It is assumed that intermediate predator only eat prey and omnivore can consume prey and intermediate predator. But, prey has the ability called as anti-predator behavior to escape from both predators. For the first discussion, it is found that all solutions are existential, uniqueness, boundedness, and non-negative. Further, we analyze the existence condition and local stability of all points, that is point for the extinction of all populations, both predators, intermediate predator, omnivore, and point for the existence of all populations. We also investigate the global stability of all points, except point for the extinction of all populations and both predators. Finally, we preform several numerical solutions by using the nonstandard Grunwald-Letnikov approximation to demonstrate the our analytical results. |
| first_indexed | 2024-04-24T19:19:27Z |
| format | Article |
| id | doaj.art-30c0aaa6438a4164b3191616ff7e2e8b |
| institution | Directory Open Access Journal |
| issn | 2549-2896 |
| language | English |
| last_indexed | 2024-04-24T19:19:27Z |
| publishDate | 2023-01-01 |
| publisher | Indonesian Bio-Mathematical Society |
| record_format | Article |
| series | Communication in Biomathematical Sciences |
| spelling | doaj.art-30c0aaa6438a4164b3191616ff7e2e8b2024-03-26T01:29:13ZengIndonesian Bio-Mathematical SocietyCommunication in Biomathematical Sciences2549-28962023-01-015212113610.5614/cbms.2022.5.2.219286Fractional-Order Food Chain Model with Omnivore and Anti-PredatorAdin Lazuardy Firdiansyah0Department of PGMI, Faculty of Tarbiyah, State Islamic Institute of Madura, Pamekasan 69371, IndonesiaA fractional-order food chain model is proposed in this article. The model is built by prey, intermediate predator, and omnivore. It is assumed that intermediate predator only eat prey and omnivore can consume prey and intermediate predator. But, prey has the ability called as anti-predator behavior to escape from both predators. For the first discussion, it is found that all solutions are existential, uniqueness, boundedness, and non-negative. Further, we analyze the existence condition and local stability of all points, that is point for the extinction of all populations, both predators, intermediate predator, omnivore, and point for the existence of all populations. We also investigate the global stability of all points, except point for the extinction of all populations and both predators. Finally, we preform several numerical solutions by using the nonstandard Grunwald-Letnikov approximation to demonstrate the our analytical results.https://journals.itb.ac.id/index.php/cbms/article/view/18694food chainfractional-ordergrunwald-letnikov approximationstability |
| spellingShingle | Adin Lazuardy Firdiansyah Fractional-Order Food Chain Model with Omnivore and Anti-Predator Communication in Biomathematical Sciences food chain fractional-order grunwald-letnikov approximation stability |
| title | Fractional-Order Food Chain Model with Omnivore and Anti-Predator |
| title_full | Fractional-Order Food Chain Model with Omnivore and Anti-Predator |
| title_fullStr | Fractional-Order Food Chain Model with Omnivore and Anti-Predator |
| title_full_unstemmed | Fractional-Order Food Chain Model with Omnivore and Anti-Predator |
| title_short | Fractional-Order Food Chain Model with Omnivore and Anti-Predator |
| title_sort | fractional order food chain model with omnivore and anti predator |
| topic | food chain fractional-order grunwald-letnikov approximation stability |
| url | https://journals.itb.ac.id/index.php/cbms/article/view/18694 |
| work_keys_str_mv | AT adinlazuardyfirdiansyah fractionalorderfoodchainmodelwithomnivoreandantipredator |