On the appearance of multiple attractors in discrete food-chains

摘要

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 Lindström [T. Lindström, On the dynamics of discrete food-chains: low- and high-frequency behavior and chaos, Journal of Mathematical Biology 45 (2002) 396–418]. 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.