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Zbl 1114.92056
Song, Xinyu; Cai, Liming; Neumann, Avidan U.
Ratio-dependent predator-prey system with stage structure for prey. (English)
[J] Discrete Contin. Dyn. Syst., Ser. B 4, No. 3, 747-758 (2004). ISSN 1531-3492; ISSN 1553-524X/e

Summary: A ratio-dependent predator-prey model with stage structure for the prey is proposed and analyzed, which improves the assumption that each individual prey has the same ability to be captured by a predator. In this paper, mathematical analysis of the model equations with regard to boundedness of solutions, nature of equilibria and permanence are analyzed. We obtain conditions that determine the permanence of the populations. Furthermore, we establish necessary and sufficient conditions for the local stability of the positive equilibrium of the model. By the application of comparing arguments and exploiting the monotonicity of one equation of the model, we obtain sufficient conditions for the global attractivity of the positive equilibrium.

MSC 2000:: *92D25 Population dynamics
34D05 Asymptotic stability of ODE
34C60 Applications of qualitative theory of ODE
92D40 Ecology

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