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Cui, Jing’an; Takeuchi, Yasuhiro

A predator-prey system with a stage structure for the prey. (English) Zbl 1132.92340

Math. Comput. Modelling 44, No. 11-12, 1126-1132 (2006).
Summary: This paper considers a periodic predator-prey system where the prey has a life history that takes the prey through two stages: immature and mature. We provide a sufficient and necessary condition to guarantee permanence of the system. It is shown that the system is permanent if and only if the growth of the predator by foraging the prey minus its death rate is positive on average during the period.

Cited in 21 Documents

MSC:

92D40 Ecology
34C25 Periodic solutions to ordinary differential equations
34D23 Global stability of solutions to ordinary differential equations
34D40 Ultimate boundedness (MSC2000)
37N25 Dynamical systems in biology

Keywords:

permanence; extinction
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\textit{J. Cui} and \textit{Y. Takeuchi}, Math. Comput. Modelling 44, No. 11--12, 1126--1132 (2006; Zbl 1132.92340)
Full Text: DOI

References:

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