Global Stability of a Predator-Prey Model with Ivlev-Type Functional Response
A predator-prey model with Ivlev-Type functional response is studied. The main purpose is to investigate the global stability of a positive (co-existence) equilibrium, whenever it exists. A recently developed approach shows that for certain classes of models, there is an implicitly defined function...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Western Libraries
2020-09-01
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| Series: | Mathematics in Applied Sciences and Engineering |
| Online Access: | https://ojs.lib.uwo.ca/index.php/mase/article/view/10794 |
| _version_ | 1818691945736699904 |
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| author | Yinshu Wu Wenzhang Huang |
| author_facet | Yinshu Wu Wenzhang Huang |
| author_sort | Yinshu Wu |
| collection | DOAJ |
| description | A predator-prey model with Ivlev-Type functional response is studied. The main purpose is to investigate the global stability of a positive (co-existence) equilibrium, whenever it exists. A recently developed approach shows that for certain classes of models, there is an implicitly defined function which plays an important rule in determining the global stability of the positive equilibrium. By performing a detailed analytic analysis we demonstrate that a crucial property of this implicitly defined function is governed by the local stability of the positive equilibrium, which enable us to show that the global and local stability of the positive equilibrium, whenever it exists, is equivalent. We believe that our approach can be extended to study the global stability of the positive equilibrium for predator-prey models with some other types of functional responses. |
| first_indexed | 2024-12-17T12:49:58Z |
| format | Article |
| id | doaj.art-3cc0a0c5ce5e436190e1a1d470be7288 |
| institution | Directory Open Access Journal |
| issn | 2563-1926 |
| language | English |
| last_indexed | 2024-12-17T12:49:58Z |
| publishDate | 2020-09-01 |
| publisher | Western Libraries |
| record_format | Article |
| series | Mathematics in Applied Sciences and Engineering |
| spelling | doaj.art-3cc0a0c5ce5e436190e1a1d470be72882022-12-21T21:47:37ZengWestern LibrariesMathematics in Applied Sciences and Engineering2563-19262020-09-011322423510.5206/mase/107944938Global Stability of a Predator-Prey Model with Ivlev-Type Functional ResponseYinshu Wu0Wenzhang HuangAlabama A&M UniversityA predator-prey model with Ivlev-Type functional response is studied. The main purpose is to investigate the global stability of a positive (co-existence) equilibrium, whenever it exists. A recently developed approach shows that for certain classes of models, there is an implicitly defined function which plays an important rule in determining the global stability of the positive equilibrium. By performing a detailed analytic analysis we demonstrate that a crucial property of this implicitly defined function is governed by the local stability of the positive equilibrium, which enable us to show that the global and local stability of the positive equilibrium, whenever it exists, is equivalent. We believe that our approach can be extended to study the global stability of the positive equilibrium for predator-prey models with some other types of functional responses.https://ojs.lib.uwo.ca/index.php/mase/article/view/10794 |
| spellingShingle | Yinshu Wu Wenzhang Huang Global Stability of a Predator-Prey Model with Ivlev-Type Functional Response Mathematics in Applied Sciences and Engineering |
| title | Global Stability of a Predator-Prey Model with Ivlev-Type Functional Response |
| title_full | Global Stability of a Predator-Prey Model with Ivlev-Type Functional Response |
| title_fullStr | Global Stability of a Predator-Prey Model with Ivlev-Type Functional Response |
| title_full_unstemmed | Global Stability of a Predator-Prey Model with Ivlev-Type Functional Response |
| title_short | Global Stability of a Predator-Prey Model with Ivlev-Type Functional Response |
| title_sort | global stability of a predator prey model with ivlev type functional response |
| url | https://ojs.lib.uwo.ca/index.php/mase/article/view/10794 |
| work_keys_str_mv | AT yinshuwu globalstabilityofapredatorpreymodelwithivlevtypefunctionalresponse AT wenzhanghuang globalstabilityofapredatorpreymodelwithivlevtypefunctionalresponse |