Persistence and attractivity in an \(N\)-species ratio-dependent predator-prey system with distributed time delays. (Q1855769)
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scientific article; zbMATH DE number 1861151
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Persistence and attractivity in an \(N\)-species ratio-dependent predator-prey system with distributed time delays. |
scientific article; zbMATH DE number 1861151 |
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Persistence and attractivity in an \(N\)-species ratio-dependent predator-prey system with distributed time delays. (English)
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28 January 2003
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The paper investigates a linear food chain with \(n\) species, in which the Michaelis-Menten predator-prey interaction is altered to include ratio-dependent predation and distributed time delays. The authors give conditions for boundedness and uniform persistence of the solutions. They further provide necessary and sufficient conditions for the existence of a unique positive equilibrium and provide conditions for its global attractivity. The latter proof is based on the construction of a suitable Lyapunov functional.
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linear food chain
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distributed time delay
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uniform persistence
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global attractivity
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