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Persistence and attractivity in an \(N\)-species ratio-dependent predator-prey system with distributed time delays. (English) Zbl 1043.34088

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.

MSC:

34K60 Qualitative investigation and simulation of models involving functional-differential equations
34K20 Stability theory of functional-differential equations
92D25 Population dynamics (general)
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