Torsten Lindström

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In this paper we derive and analyze a discrete version of Rosenzweig's (Am. Nat. 1973) food-chain model. We provide substantial analytical and numerical evidence for the general dynamical patterns of food chains predicted by De Feo and Rinaldi (Am. Nat. 1997) remaining largely unaffected by this discretization. Our theoretical analysis gives rise to a(More)
The Rosenzweig-MacArthur (1963) criterion is a graphical criterion that has been widely used for elucidating the local stability properties of the Gause (1934) type predator-prey systems. It has not been stated whether a similar criterion holds for models with explicit resource dynamics (Kooi et al. (1998)), like the chemostat model. In this paper we use(More)
On infinitesimally short time intervals various processes contributing to population change tend to operate independently so that we can simply add their contributions (Metz and Diekmann, The dynamics of physiologically structured populations, 1986, p. 3). This is one of the cornerstones for differential equations modeling in general. Complicated models for(More)
Klebanoff and Hastings [A. Klebanoff, A. Hastings, Chaos in three species food chains, Journal of Mathematical Biology 32 (1994) 427–451] detected cases of multiple attractors in continuous food-chains. In this paper we discuss similar phenomena in the discrete food-chains introduced by Lindströ m [T. Lindströ m, On the dynamics of discrete food-chains:(More)
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