A Lotka--Volterra type food chain model with stage structure and time delays (Q819028)
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scientific article; zbMATH DE number 5014227
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A Lotka--Volterra type food chain model with stage structure and time delays |
scientific article; zbMATH DE number 5014227 |
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A Lotka--Volterra type food chain model with stage structure and time delays (English)
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22 March 2006
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A three species Lotka-Volterra-type food chain model with mature and immature species and delay is investigated. First, the positivity of the solutions is proved. Then, sufficient conditions for the permanence of the solutions are given. Equilibrium solutions of the system are found. They represent the total annihilation of the system (E0), the annihilation of predators (E1), the annihilation of the top prey only (E2) and the coexistence of all species (E*). Sufficient conditions for the global stability of E1, E2, E* are derived. A related paper is given by \textit{J. F. M. Al-Omari} and \textit{S. A. Gourley} [Nonlinear Anal., Real World Appl. 6, 13--33 (2005; Zbl 1088.34070)].
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global stability
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permanence
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delay
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stage structured
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