Dynamic Behaviors of a Discrete Two Species Predator-Prey System Incorporating Harvesting
A discrete two species predator-prey captured system is studied. Firstly, a sufficient condition of a positive equilibrium point for this system is obtained. Secondly, we observe that the two nonnegative equilibriums of the system are unstable through the eigenvalue discriminant method, and the posi...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2012/429076 |
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| _version_ | 1832561295623192576 |
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| author | Ting Wu |
| author_facet | Ting Wu |
| author_sort | Ting Wu |
| collection | DOAJ |
| description | A discrete two species predator-prey captured system is studied. Firstly, a sufficient condition of a positive equilibrium point for this system is obtained. Secondly, we observe that the two nonnegative equilibriums of the system are unstable through the eigenvalue discriminant method, and the positive equilibrium point is asymptotically stable by Jury criterion. Lastly, we obtain the optimal capture strategy of the system from the maximum principle by constructing a discrete Hamiltonian function. To show the feasibility of the main results, a suitable example together with its numerical simulations is illustrated in the last part of the paper. The example with certain practical significance might give an optimal scheme of the greatest economic benefits for the captors. |
| format | Article |
| id | doaj-art-86eb2022e90b4683be9dc90ede0f8fd5 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-86eb2022e90b4683be9dc90ede0f8fd52025-02-03T01:25:23ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2012-01-01201210.1155/2012/429076429076Dynamic Behaviors of a Discrete Two Species Predator-Prey System Incorporating HarvestingTing Wu0Department of Mathematics, Minjiang University, Fujian, Fuzhou 350108, ChinaA discrete two species predator-prey captured system is studied. Firstly, a sufficient condition of a positive equilibrium point for this system is obtained. Secondly, we observe that the two nonnegative equilibriums of the system are unstable through the eigenvalue discriminant method, and the positive equilibrium point is asymptotically stable by Jury criterion. Lastly, we obtain the optimal capture strategy of the system from the maximum principle by constructing a discrete Hamiltonian function. To show the feasibility of the main results, a suitable example together with its numerical simulations is illustrated in the last part of the paper. The example with certain practical significance might give an optimal scheme of the greatest economic benefits for the captors.http://dx.doi.org/10.1155/2012/429076 |
| spellingShingle | Ting Wu Dynamic Behaviors of a Discrete Two Species Predator-Prey System Incorporating Harvesting Discrete Dynamics in Nature and Society |
| title | Dynamic Behaviors of a Discrete Two Species Predator-Prey System Incorporating Harvesting |
| title_full | Dynamic Behaviors of a Discrete Two Species Predator-Prey System Incorporating Harvesting |
| title_fullStr | Dynamic Behaviors of a Discrete Two Species Predator-Prey System Incorporating Harvesting |
| title_full_unstemmed | Dynamic Behaviors of a Discrete Two Species Predator-Prey System Incorporating Harvesting |
| title_short | Dynamic Behaviors of a Discrete Two Species Predator-Prey System Incorporating Harvesting |
| title_sort | dynamic behaviors of a discrete two species predator prey system incorporating harvesting |
| url | http://dx.doi.org/10.1155/2012/429076 |
| work_keys_str_mv | AT tingwu dynamicbehaviorsofadiscretetwospeciespredatorpreysystemincorporatingharvesting |