Chaos in three species food chains |
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| Authors: | Aaron Klebanoff Alan Hastings |
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| Institution: | (1) Institute of Theoretical Dynamics, University of California, 95616 Davis, CA, USA;(2) Division of Environmental Studies, Institute of Theoretical Dynamics, and Center for Population Biology, University of California, 95616 Davis, CA, USA;(3) Present address: Department of Mathematics, Rose-Hulman Institute of Technology, Wabash Avenue, 5500 Terre Haute, IN 47803, USA |
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| Abstract: | We study the dynamics of a three species food chain using bifurcation theory to demonstrate the existence of chaotic dynamics in the neighborhood of the equilibrium where the top species in the food chain is absent. The goal of our study is to demonstrate the presence of chaos in a class of ecological models, rather than just in a specific model. This work extends earlier numerical studies of a particular system by Hastings and Powell (1991) by showing that chaos occurs in a class of ecological models. The mathematical techniques we use are based on work by Guckenheimer and Holmes (1983) on co-dimension two bifurcations. However, restrictions on the equations we study imposed by ecological assumptions require a new and somewhat different analysis. |
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| Keywords: | Chaos Food chain Bifurcation Normal form |
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