Stability analysis of predator - prey population model with time delay and constant rate of harvesting
This paper studies the effect of time delay and harvesting on the dynamics of the predator - prey model with a time delay in the growth rate of the prey equation. The predator and prey are then harvested with constant rates. The constant rates may drive the model to one, two, or none positive equil...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English English |
| Published: |
University of the Punjab Lahore
2008
|
| Subjects: | |
| Online Access: | http://psasir.upm.edu.my/id/eprint/16821/1/Stability%20analysis%20of%20predator.pdf |
| _version_ | 1825945890070724608 |
|---|---|
| author | Toaha, Syamsuddin Abu Hassan, Malik |
| author_facet | Toaha, Syamsuddin Abu Hassan, Malik |
| author_sort | Toaha, Syamsuddin |
| collection | UPM |
| description | This paper studies the effect of time delay and harvesting on the dynamics of the predator - prey model with a time delay in the growth rate of the prey equation. The predator and prey are then harvested with constant rates. The constant rates may drive the model to one, two, or
none positive equilibrium points. When there exist two positive equilibrium points, one of them is possibly stable. In the case of the constant rates are quite small and the equilibrium point is not stable, an asymptotically
stable limit cycle occurs. The result showed that the time delay can induce instability of the stable equilibrium point, Hopf bifurcation and stability switches. |
| first_indexed | 2024-03-06T07:38:33Z |
| format | Article |
| id | upm.eprints-16821 |
| institution | Universiti Putra Malaysia |
| language | English English |
| last_indexed | 2024-03-06T07:38:33Z |
| publishDate | 2008 |
| publisher | University of the Punjab Lahore |
| record_format | dspace |
| spelling | upm.eprints-168212016-01-20T08:46:46Z http://psasir.upm.edu.my/id/eprint/16821/ Stability analysis of predator - prey population model with time delay and constant rate of harvesting Toaha, Syamsuddin Abu Hassan, Malik This paper studies the effect of time delay and harvesting on the dynamics of the predator - prey model with a time delay in the growth rate of the prey equation. The predator and prey are then harvested with constant rates. The constant rates may drive the model to one, two, or none positive equilibrium points. When there exist two positive equilibrium points, one of them is possibly stable. In the case of the constant rates are quite small and the equilibrium point is not stable, an asymptotically stable limit cycle occurs. The result showed that the time delay can induce instability of the stable equilibrium point, Hopf bifurcation and stability switches. University of the Punjab Lahore 2008 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/16821/1/Stability%20analysis%20of%20predator.pdf Toaha, Syamsuddin and Abu Hassan, Malik (2008) Stability analysis of predator - prey population model with time delay and constant rate of harvesting. Punjub University Journal of Mathematics, 40. pp. 37-48. ISSN 1016-2526 http://pu.edu.pk/home/journal/29 Lotka-Volterra equations Biology - Mathematical models Harvesting English |
| spellingShingle | Lotka-Volterra equations Biology - Mathematical models Harvesting Toaha, Syamsuddin Abu Hassan, Malik Stability analysis of predator - prey population model with time delay and constant rate of harvesting |
| title | Stability analysis of predator - prey population model with time delay and constant rate of harvesting |
| title_full | Stability analysis of predator - prey population model with time delay and constant rate of harvesting |
| title_fullStr | Stability analysis of predator - prey population model with time delay and constant rate of harvesting |
| title_full_unstemmed | Stability analysis of predator - prey population model with time delay and constant rate of harvesting |
| title_short | Stability analysis of predator - prey population model with time delay and constant rate of harvesting |
| title_sort | stability analysis of predator prey population model with time delay and constant rate of harvesting |
| topic | Lotka-Volterra equations Biology - Mathematical models Harvesting |
| url | http://psasir.upm.edu.my/id/eprint/16821/1/Stability%20analysis%20of%20predator.pdf |
| work_keys_str_mv | AT toahasyamsuddin stabilityanalysisofpredatorpreypopulationmodelwithtimedelayandconstantrateofharvesting AT abuhassanmalik stabilityanalysisofpredatorpreypopulationmodelwithtimedelayandconstantrateofharvesting |