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Zbl 0823.92030
Klebanoff, Aaron; Hastings, Alan
Chaos in three species food chains.
(English)
[J] J. Math. Biol. 32, No.5, 427-451 (1994). ISSN 0303-6812; ISSN 1432-1416/e

Summary: 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. \par This work extends earlier numerical studies of a particular system by {\it A. Hastings} and {\it T. Powell} [Ecology 72, No. 3, 896-903 (1991)] by showing that chaos occurs in a class of ecological models. The mathematical techniques we use are based on work by {\it J. Guckenheimer} and {\it P. Holmes} [Nonlinear oscillations, dynamical systems, and bifurcations of vector fields (1983; Zbl 0515.34001)] on co-dimension two bifurcations. However, restrictions on the equations we study imposed by ecological assumptions require a new and somewhat different analysis.
MSC 2000:
*92D40 Ecology
37N99 Applications of dynamical systems
37D45 Strange attractors, chaotic dynamics
37G99 Bifurcation theory

Keywords: normal form; three species food chain; chaos; bifurcations

Citations: Zbl 0515.34001

Cited in: Zbl 1109.92051

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