Analysis of The Rosenzweig-MacArthur Predator-Prey Model with Anti-Predator Behavior
This paper discusses the analysis of the Rosenzweig-MacArthur predator-prey model with anti-predator behavior. The analysis is started by determining the equilibrium points, existence, and conditions of the stability. Identifying the type of Hopf bifurcation by using the divergence criterion. It has...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Mathematics Department UIN Maulana Malik Ibrahim Malang
2021-05-01
|
| Series: | Cauchy: Jurnal Matematika Murni dan Aplikasi |
| Subjects: | |
| Online Access: | https://ejournal.uin-malang.ac.id/index.php/Math/article/view/11472 |
| _version_ | 1811249792225902592 |
|---|---|
| author | Ismail Djakaria Muhammad Bachtiar Gaib Resmawan Resmawan |
| author_facet | Ismail Djakaria Muhammad Bachtiar Gaib Resmawan Resmawan |
| author_sort | Ismail Djakaria |
| collection | DOAJ |
| description | This paper discusses the analysis of the Rosenzweig-MacArthur predator-prey model with anti-predator behavior. The analysis is started by determining the equilibrium points, existence, and conditions of the stability. Identifying the type of Hopf bifurcation by using the divergence criterion. It has shown that the model has three equilibrium points, i.e., the extinction of population equilibrium point (E0), the non-predatory equilibrium point (E1), and the co-existence equilibrium point (E2). The existence and stability of each equilibrium point can be shown by satisfying several conditions of parameters. The divergence criterion indicates the existence of the supercritical Hopf-bifurcation around the equilibrium point E2. Finally, our model's dynamics population is confirmed by our numerical simulations by using the 4th-order Runge-Kutta methods. |
| first_indexed | 2024-04-12T15:52:46Z |
| format | Article |
| id | doaj.art-3c614725f5684909aa1222d885a6d20c |
| institution | Directory Open Access Journal |
| issn | 2086-0382 2477-3344 |
| language | English |
| last_indexed | 2024-04-12T15:52:46Z |
| publishDate | 2021-05-01 |
| publisher | Mathematics Department UIN Maulana Malik Ibrahim Malang |
| record_format | Article |
| series | Cauchy: Jurnal Matematika Murni dan Aplikasi |
| spelling | doaj.art-3c614725f5684909aa1222d885a6d20c2022-12-22T03:26:27ZengMathematics Department UIN Maulana Malik Ibrahim MalangCauchy: Jurnal Matematika Murni dan Aplikasi2086-03822477-33442021-05-016426026910.18860/ca.v6i4.114725640Analysis of The Rosenzweig-MacArthur Predator-Prey Model with Anti-Predator BehaviorIsmail Djakaria0Muhammad Bachtiar Gaib1Resmawan Resmawan2Department of Mathematics, Universitas Negeri GorontaloDepartment of Mathematics, Universitas Negeri GorontaloDepartment of Mathematics, Universitas Negeri GorontaloThis paper discusses the analysis of the Rosenzweig-MacArthur predator-prey model with anti-predator behavior. The analysis is started by determining the equilibrium points, existence, and conditions of the stability. Identifying the type of Hopf bifurcation by using the divergence criterion. It has shown that the model has three equilibrium points, i.e., the extinction of population equilibrium point (E0), the non-predatory equilibrium point (E1), and the co-existence equilibrium point (E2). The existence and stability of each equilibrium point can be shown by satisfying several conditions of parameters. The divergence criterion indicates the existence of the supercritical Hopf-bifurcation around the equilibrium point E2. Finally, our model's dynamics population is confirmed by our numerical simulations by using the 4th-order Runge-Kutta methods.https://ejournal.uin-malang.ac.id/index.php/Math/article/view/11472rosenzweig-macarthurpredator-prey modelanti-predator behaviourhopf bifurcationdivergence criterionequilibrium point. |
| spellingShingle | Ismail Djakaria Muhammad Bachtiar Gaib Resmawan Resmawan Analysis of The Rosenzweig-MacArthur Predator-Prey Model with Anti-Predator Behavior Cauchy: Jurnal Matematika Murni dan Aplikasi rosenzweig-macarthur predator-prey model anti-predator behaviour hopf bifurcation divergence criterion equilibrium point. |
| title | Analysis of The Rosenzweig-MacArthur Predator-Prey Model with Anti-Predator Behavior |
| title_full | Analysis of The Rosenzweig-MacArthur Predator-Prey Model with Anti-Predator Behavior |
| title_fullStr | Analysis of The Rosenzweig-MacArthur Predator-Prey Model with Anti-Predator Behavior |
| title_full_unstemmed | Analysis of The Rosenzweig-MacArthur Predator-Prey Model with Anti-Predator Behavior |
| title_short | Analysis of The Rosenzweig-MacArthur Predator-Prey Model with Anti-Predator Behavior |
| title_sort | analysis of the rosenzweig macarthur predator prey model with anti predator behavior |
| topic | rosenzweig-macarthur predator-prey model anti-predator behaviour hopf bifurcation divergence criterion equilibrium point. |
| url | https://ejournal.uin-malang.ac.id/index.php/Math/article/view/11472 |
| work_keys_str_mv | AT ismaildjakaria analysisoftherosenzweigmacarthurpredatorpreymodelwithantipredatorbehavior AT muhammadbachtiargaib analysisoftherosenzweigmacarthurpredatorpreymodelwithantipredatorbehavior AT resmawanresmawan analysisoftherosenzweigmacarthurpredatorpreymodelwithantipredatorbehavior |