Rai, Bindhyachal; Freedman, H. I.; Addicott, John F. Analysis of three species models of mutualism in predator-prey and competitive systems. (English) Zbl 0532.92025 Math. Biosci. 65, 13-50 (1983). An interaction among several different species is mutualistic if the presence of each species enhances the per capita growth rate of the other. In this paper, the authors present two models of mutualism in which interactions among three species lead to mutualism between two of them. The first model is governed by the system \(u'=uh(u,x)\), \(x'=\alpha xg(u,x)-yp(u,x)\), \(y'=y(-s+cp(u,x))\), and the second one by \(u'=uh(u,x_ 1)\), x’\({}_ 1=\alpha x_ 1(g_ 1(u,x_ 1)-q_ 1(u,x_ 1,x_ 2))\), x’\({}_ 2=x_ 2(g_ 2(x_ 2)-q_ 2(x_ 1,x_ 2)).\) Under several assumptions which correspond to biological constraints they study the existence of equilibria and their local stability and discuss the existence of periodic solutions surrounding the equilibria. Also some interesting special cases of the two systems are examined in details, while an informed nice discussion for several situations of the two models completes the paper. Reviewer: G.Karakostas Cited in 2 ReviewsCited in 38 Documents MSC: 92D25 Population dynamics (general) 34C25 Periodic solutions to ordinary differential equations 34D30 Structural stability and analogous concepts of solutions to ordinary differential equations 34D05 Asymptotic properties of solutions to ordinary differential equations Keywords:three species models of mutualism; competitive systems; equilibria; Hopf bifurcation; predator-prey models PDFBibTeX XMLCite \textit{B. Rai} et al., Math. Biosci. 65, 13--50 (1983; Zbl 0532.92025) Full Text: DOI References: [1] Addicott, J. F., A multispecies aphid-ant association: Density dependence and species-specific effects, Canad. J. Zool., 57, 558-569 (1979) [2] Addicott, J. 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