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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)
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)
We argue that any attempt to classify dynamical properties from nonlinear finite time-series data requires a mechanistic model fitting the data better than piecewise linear models according to standard model selection criteria. Such a procedure seems necessary but still not sufficient.