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On the appearance of multiple attractors in discrete food-chains. (English) Zbl 1109.92051

Summary: A. Klebanoff and A. Hastings [Chaos in three species food chains. J. Math. Biol. 32, 427–451 (1994; Zbl 0823.92030)] detected cases of multiple attractors in continuous food-chains. We discuss similar phenomena in the discrete food-chains introduced by T. Lindström [On the dynamics of discrete food-chains: low- and high-frequency behavior and optimality of chaos. ibid. 45, No. 5, 396–418 (2002; Zbl 1012.92043)]. The results imply that the dynamical properties including species persistence may change due to disturbances that do not involve changes in the environmental parameters. Thus, there are possibilities that species may be eradicated or start to oscillate at different frequencies without any changes in the environment. Since this is now shown to hold in both seasonal and non-seasonal environments, we expect that this is a rather general property of ecosystems.

MSC:

92D40 Ecology
37N25 Dynamical systems in biology

Software:

AnT 4.669
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Full Text: DOI

References:

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