Convergences of a stage-structured predator-prey model with modified Leslie-Gower and Holling-type II schemes. (English) Zbl 1419.34158
Summary: A stage-structured predator-prey model (stage structure for both predator and prey) with modified Leslie-Gower and Holling-II schemes is studied in this paper. Using the iterative technique method and the fluctuation lemma, sufficient conditions which guarantee the global stability of the positive equilibrium and boundary equilibrium are obtained. Our results indicate that for a stage-structured predator-prey community, both the stage structure and the death rate of the mature species are the important factors that lead to the permanence or extinction of the system.
MSC:
| 34D23 | Global stability of solutions to ordinary differential equations |
| 92B05 | General biology and biomathematics |
| 34D05 | Asymptotic properties of solutions to ordinary differential equations |
| 92D25 | Population dynamics (general) |
Keywords:
global stability; extinction; stage-structure; Leslie-Gower; Holling-type II; predator-preyReferences:
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