Song, Xinyu; Cai, Liming; Neumann, Avidan U. Ratio-dependent predator-prey system with stage structure for prey. (English) Zbl 1114.92056 Discrete Contin. Dyn. Syst., Ser. B 4, No. 3, 747-758 (2004). 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. Cited in 18 Documents MSC: 92D25 Population dynamics (general) 34D05 Asymptotic properties of solutions to ordinary differential equations 34C60 Qualitative investigation and simulation of ordinary differential equation models 92D40 Ecology PDFBibTeX XMLCite \textit{X. Song} et al., Discrete Contin. Dyn. Syst., Ser. B 4, No. 3, 747--758 (2004; Zbl 1114.92056) Full Text: DOI