A universal bifurcation diagram for seasonally perturbed predator-prey models
The bifurcations of a periodically forced predator-prey model (the chemostat model), with a prey feeding on a limiting nutrient, are numerically detected with a continuation technique. Eight bifurcation diagrams are produced (one for each parameter in the model) and shown to be topologically equivalent. These diagrams are also equivalent to those of the most commonly used predator-prey model (the Rosenzweig-McArthur model). Thus, all basic modes of behavior of the two main predator-prey models can be explained by means of a single bifurcation diagram.
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- Afrajmovich, V. S., V. I. Arnold, Yu. S. Il'ashenko and P. Shinlnikov. 1991. Bifurcation theory. InDynamical Systems, Vol. 5, V. I. Arnold (Ed.),Encyclopaedia of Mathematical Sciences. New York: Springer Verlag.Google Scholar
- Allen, J. C. 1989. Are natural enemy populations chaotic? InEstimation and Analysis of Insect Populations, Lecture Notes in Statistics, Vol. 55, L. McDonald, B. Manly, J. Lockwood and J. Logan (Eds), pp. 190–205. New York: Springer Verlag.Google Scholar
- Guckenheimer, J. and P. Holmes. 1983.Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields. New York: Springer Verlag.Google Scholar
- Hastings, A., C. L. Hom, S. Ellner, P. Turchin and H. C. J. Godfray. 1993. Chaos in ecology: is mother nature a strange attractor?Ann. Rev. Ecol. Syst. 24, 1–33.Google Scholar
- Schaffer, W. M. 1988. Perceiving order in the chaos of nature. InEvolution of Life Histories of Mammals, M. S. Boyce (Ed.), pp. 313–350. New Haven: Yale University Press.Google Scholar
- Toro, M. and J. Aracil. 1988. Qualitative analysis of system dynamics ecological models.Syst. Dyn. Rev. 4, 56–80.Google Scholar