Global Stability and Hopf Bifurcation of a Predator-Prey Model with Time Delay and Stage Structure
A delayed predator-prey system with Holling type II functional response and stage structure for both the predator and the prey is investigated. By analyzing the corresponding characteristic equations, the local stability of each of the feasible equilibria of the system is addressed and the existence...
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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/10.1155/2014/431671 |
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| _version_ | 1832560379625996288 |
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| author | Lingshu Wang Guanghui Feng |
| author_facet | Lingshu Wang Guanghui Feng |
| author_sort | Lingshu Wang |
| collection | DOAJ |
| description | A delayed predator-prey system with Holling type II functional response and stage structure for both the predator and the prey is investigated. By analyzing the corresponding characteristic equations, the local stability of each of the feasible equilibria of the system is addressed and the existence of a Hopf bifurcation at the coexistence equilibrium is established. By means of persistence theory on infinite dimensional systems, it is proved that the system is permanent. By using Lyapunov functions and the LaSalle invariant principle, the global stability of each of the feasible equilibria of the model is discussed. Numerical simulations are carried out to illustrate the main theoretical results. |
| format | Article |
| id | doaj-art-4f9a5161c6f7466783067ac21160cd71 |
| 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-4f9a5161c6f7466783067ac21160cd712025-02-03T01:27:39ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/431671431671Global Stability and Hopf Bifurcation of a Predator-Prey Model with Time Delay and Stage StructureLingshu Wang0Guanghui Feng1School of Mathematics and Statistics, Hebei University of Economics & Business, Shijiazhuang 050061, ChinaDepartment of Basic Courses, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, ChinaA delayed predator-prey system with Holling type II functional response and stage structure for both the predator and the prey is investigated. By analyzing the corresponding characteristic equations, the local stability of each of the feasible equilibria of the system is addressed and the existence of a Hopf bifurcation at the coexistence equilibrium is established. By means of persistence theory on infinite dimensional systems, it is proved that the system is permanent. By using Lyapunov functions and the LaSalle invariant principle, the global stability of each of the feasible equilibria of the model is discussed. Numerical simulations are carried out to illustrate the main theoretical results.http://dx.doi.org/10.1155/2014/431671 |
| spellingShingle | Lingshu Wang Guanghui Feng Global Stability and Hopf Bifurcation of a Predator-Prey Model with Time Delay and Stage Structure Journal of Applied Mathematics |
| title | Global Stability and Hopf Bifurcation of a Predator-Prey Model with Time Delay and Stage Structure |
| title_full | Global Stability and Hopf Bifurcation of a Predator-Prey Model with Time Delay and Stage Structure |
| title_fullStr | Global Stability and Hopf Bifurcation of a Predator-Prey Model with Time Delay and Stage Structure |
| title_full_unstemmed | Global Stability and Hopf Bifurcation of a Predator-Prey Model with Time Delay and Stage Structure |
| title_short | Global Stability and Hopf Bifurcation of a Predator-Prey Model with Time Delay and Stage Structure |
| title_sort | global stability and hopf bifurcation of a predator prey model with time delay and stage structure |
| url | http://dx.doi.org/10.1155/2014/431671 |
| work_keys_str_mv | AT lingshuwang globalstabilityandhopfbifurcationofapredatorpreymodelwithtimedelayandstagestructure AT guanghuifeng globalstabilityandhopfbifurcationofapredatorpreymodelwithtimedelayandstagestructure |