Stability Analysis of a Ratio-Dependent Predator-Prey Model Incorporating a Prey Refuge
A ratio-dependent predator-prey model incorporating a prey refuge with disease in the prey population is formulated and analyzed. The effects of time delay due to the gestation of the predator and stage structure for the predator on the dynamics of the system are concerned. By analyzing the correspo...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/978758 |
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| _version_ | 1832558211810459648 |
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| author | Lingshu Wang Guanghui Feng |
| author_facet | Lingshu Wang Guanghui Feng |
| author_sort | Lingshu Wang |
| collection | DOAJ |
| description | A ratio-dependent predator-prey model incorporating a prey refuge with disease in the prey population is formulated and analyzed. The effects of time delay due to the gestation of the predator and stage structure for the predator on the dynamics of the system are concerned. By analyzing the corresponding characteristic equations, the local stability of a predator-extinction equilibrium and a coexistence equilibrium of the system is discussed, respectively. Further, it is proved that the system undergoes a Hopf bifurcation at the coexistence equilibrium, when τ=τ0. By comparison arguments, sufficient conditions are obtained for the global stability of the predator-extinction equilibrium. By using an iteration technique, sufficient conditions are derived for the global attractivity of the coexistence equilibrium of the proposed system. |
| format | Article |
| id | doaj-art-e7850854c000481ba46d99a0ddcf8528 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-e7850854c000481ba46d99a0ddcf85282025-02-03T01:33:05ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/978758978758Stability Analysis of a Ratio-Dependent Predator-Prey Model Incorporating a Prey RefugeLingshu Wang0Guanghui Feng1School of Mathematics and Statistics, Hebei University of Economics & Business, Shijiazhuang 050061, ChinaInstitute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, ChinaA ratio-dependent predator-prey model incorporating a prey refuge with disease in the prey population is formulated and analyzed. The effects of time delay due to the gestation of the predator and stage structure for the predator on the dynamics of the system are concerned. By analyzing the corresponding characteristic equations, the local stability of a predator-extinction equilibrium and a coexistence equilibrium of the system is discussed, respectively. Further, it is proved that the system undergoes a Hopf bifurcation at the coexistence equilibrium, when τ=τ0. By comparison arguments, sufficient conditions are obtained for the global stability of the predator-extinction equilibrium. By using an iteration technique, sufficient conditions are derived for the global attractivity of the coexistence equilibrium of the proposed system.http://dx.doi.org/10.1155/2014/978758 |
| spellingShingle | Lingshu Wang Guanghui Feng Stability Analysis of a Ratio-Dependent Predator-Prey Model Incorporating a Prey Refuge Journal of Applied Mathematics |
| title | Stability Analysis of a Ratio-Dependent Predator-Prey Model Incorporating a Prey Refuge |
| title_full | Stability Analysis of a Ratio-Dependent Predator-Prey Model Incorporating a Prey Refuge |
| title_fullStr | Stability Analysis of a Ratio-Dependent Predator-Prey Model Incorporating a Prey Refuge |
| title_full_unstemmed | Stability Analysis of a Ratio-Dependent Predator-Prey Model Incorporating a Prey Refuge |
| title_short | Stability Analysis of a Ratio-Dependent Predator-Prey Model Incorporating a Prey Refuge |
| title_sort | stability analysis of a ratio dependent predator prey model incorporating a prey refuge |
| url | http://dx.doi.org/10.1155/2014/978758 |
| work_keys_str_mv | AT lingshuwang stabilityanalysisofaratiodependentpredatorpreymodelincorporatingapreyrefuge AT guanghuifeng stabilityanalysisofaratiodependentpredatorpreymodelincorporatingapreyrefuge |