The local Bifurcation of Dynamic Behavior of Predator-Prey System with Refuge for both Species
The main purpose of this paper is to study a predator – prey dynamical system consisting of three species prey, specialized predator and generalist predator namely H (t), I (t) and J (t) respectively, w food web and refuge for the prey and specialized predator population. The consider system has fi...
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University of Baghdad
2025-01-01
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| Series: | Ibn Al-Haitham Journal for Pure and Applied Sciences |
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| Online Access: | https://jih.uobaghdad.edu.iq/index.php/j/article/view/3461 |
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| author | Intsar Matlob Saad Naji |
| author_facet | Intsar Matlob Saad Naji |
| author_sort | Intsar Matlob |
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The main purpose of this paper is to study a predator – prey dynamical system consisting of three species prey, specialized predator and generalist predator namely H (t), I (t) and J (t) respectively, w food web and refuge for the prey and specialized predator population. The consider system has five equilibrium points A0=(0, 0, 0), A1=(1, 0, 0), A2=(h, i, 0), A3=(h, 0, j), and the positive equilibrium point A4=(h, i, j) .The stability and bifurcation of the equilibrium points was studied and the main influence was the qualitative behavior of the solution. It was found that A0 was unstable while the other equilibrium points are stable under condition so we study their bifurcation and we show that A1,A2,and A3 are transcritical while A, is saddle node bifurcation. Numerical simulations were used to illustrate the occurrence of local bifurcation of this model.
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| format | Article |
| id | doaj-art-56e5b0077a2d407298e3af56602be742 |
| institution | Kabale University |
| issn | 1609-4042 2521-3407 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | University of Baghdad |
| record_format | Article |
| series | Ibn Al-Haitham Journal for Pure and Applied Sciences |
| spelling | doaj-art-56e5b0077a2d407298e3af56602be7422025-01-22T01:21:09ZengUniversity of BaghdadIbn Al-Haitham Journal for Pure and Applied Sciences1609-40422521-34072025-01-0138110.30526/38.1.3461The local Bifurcation of Dynamic Behavior of Predator-Prey System with Refuge for both Species Intsar Matlob0https://orcid.org/0009-0002-4001-8873Saad Naji1https://orcid.org/0000-0002-6865-9798Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq.Department of Mathematics, College of Science for Women, University of Baghdad, Iraq. The main purpose of this paper is to study a predator – prey dynamical system consisting of three species prey, specialized predator and generalist predator namely H (t), I (t) and J (t) respectively, w food web and refuge for the prey and specialized predator population. The consider system has five equilibrium points A0=(0, 0, 0), A1=(1, 0, 0), A2=(h, i, 0), A3=(h, 0, j), and the positive equilibrium point A4=(h, i, j) .The stability and bifurcation of the equilibrium points was studied and the main influence was the qualitative behavior of the solution. It was found that A0 was unstable while the other equilibrium points are stable under condition so we study their bifurcation and we show that A1,A2,and A3 are transcritical while A, is saddle node bifurcation. Numerical simulations were used to illustrate the occurrence of local bifurcation of this model. https://jih.uobaghdad.edu.iq/index.php/j/article/view/3461Local bifurcationpredator-perystability analysisLyapunov's functionecologicalRefuge |
| spellingShingle | Intsar Matlob Saad Naji The local Bifurcation of Dynamic Behavior of Predator-Prey System with Refuge for both Species Ibn Al-Haitham Journal for Pure and Applied Sciences Local bifurcation predator-pery stability analysis Lyapunov's function ecological Refuge |
| title | The local Bifurcation of Dynamic Behavior of Predator-Prey System with Refuge for both Species |
| title_full | The local Bifurcation of Dynamic Behavior of Predator-Prey System with Refuge for both Species |
| title_fullStr | The local Bifurcation of Dynamic Behavior of Predator-Prey System with Refuge for both Species |
| title_full_unstemmed | The local Bifurcation of Dynamic Behavior of Predator-Prey System with Refuge for both Species |
| title_short | The local Bifurcation of Dynamic Behavior of Predator-Prey System with Refuge for both Species |
| title_sort | local bifurcation of dynamic behavior of predator prey system with refuge for both species |
| topic | Local bifurcation predator-pery stability analysis Lyapunov's function ecological Refuge |
| url | https://jih.uobaghdad.edu.iq/index.php/j/article/view/3461 |
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