Stability and Bifurcation Analysis on an Ecoepidemiological Model with Stage Structure and Time Delay
An ecoepidemiological predator-prey model with stage structure for the predator and time delay due to the gestation of the predator is investigated. The effects of a prey refuge with disease in the prey population are concerned. By analyzing the corresponding characteristic equations, the local stab...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/727818 |
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| _version_ | 1832545580134432768 |
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| author | Lingshu Wang Guanghui Feng |
| author_facet | Lingshu Wang Guanghui Feng |
| author_sort | Lingshu Wang |
| collection | DOAJ |
| description | An ecoepidemiological predator-prey model with stage structure for the predator and time delay due to the gestation of the predator is investigated. The effects of a prey refuge with disease in the prey population are concerned. By analyzing the corresponding characteristic equations, the local stability of each of the feasible equilibria of the model is discussed. Further, it is proved that the model undergoes a Hopf bifurcation at the positive equilibrium. By means of appropriate Lyapunov functions and LaSalle’s invariance principle, sufficient conditions are obtained for the global stability of the semitrivial boundary equilibria. By using an iteration technique, sufficient conditions are derived for the global attractiveness of the positive equilibrium. |
| format | Article |
| id | doaj-art-6f446def72024387adaf04730bd58802 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-6f446def72024387adaf04730bd588022025-02-03T07:25:23ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/727818727818Stability and Bifurcation Analysis on an Ecoepidemiological Model with Stage Structure and Time DelayLingshu Wang0Guanghui Feng1School of Mathematics and Statistics, Hebei University of Economics & Business, Shijiazhuang 050061, ChinaInstitute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, ChinaAn ecoepidemiological predator-prey model with stage structure for the predator and time delay due to the gestation of the predator is investigated. The effects of a prey refuge with disease in the prey population are concerned. By analyzing the corresponding characteristic equations, the local stability of each of the feasible equilibria of the model is discussed. Further, it is proved that the model undergoes a Hopf bifurcation at the positive equilibrium. By means of appropriate Lyapunov functions and LaSalle’s invariance principle, sufficient conditions are obtained for the global stability of the semitrivial boundary equilibria. By using an iteration technique, sufficient conditions are derived for the global attractiveness of the positive equilibrium.http://dx.doi.org/10.1155/2014/727818 |
| spellingShingle | Lingshu Wang Guanghui Feng Stability and Bifurcation Analysis on an Ecoepidemiological Model with Stage Structure and Time Delay Abstract and Applied Analysis |
| title | Stability and Bifurcation Analysis on an Ecoepidemiological Model with Stage Structure and Time Delay |
| title_full | Stability and Bifurcation Analysis on an Ecoepidemiological Model with Stage Structure and Time Delay |
| title_fullStr | Stability and Bifurcation Analysis on an Ecoepidemiological Model with Stage Structure and Time Delay |
| title_full_unstemmed | Stability and Bifurcation Analysis on an Ecoepidemiological Model with Stage Structure and Time Delay |
| title_short | Stability and Bifurcation Analysis on an Ecoepidemiological Model with Stage Structure and Time Delay |
| title_sort | stability and bifurcation analysis on an ecoepidemiological model with stage structure and time delay |
| url | http://dx.doi.org/10.1155/2014/727818 |
| work_keys_str_mv | AT lingshuwang stabilityandbifurcationanalysisonanecoepidemiologicalmodelwithstagestructureandtimedelay AT guanghuifeng stabilityandbifurcationanalysisonanecoepidemiologicalmodelwithstagestructureandtimedelay |