Oscillations of a Biotic Species Feeding on an Abiotic Resource

E. Beretta, G. I. Bischi and F. Solimano
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E. Beretta: University of Urbino, Institute of Biomathematics
G. I. Bischi: University of Urbino, Institute of Biomathematics
F. Solimano: University of Urbino, Institute of Biomathematics

A chapter in Biomathematics and Related Computational Problems, 1988, pp 121-131 from Springer

Abstract: Abstract We study a simple model of an open system with a constant input of an abiotic resource on which a biotic species is feeding, and we assume that part of the dead biomass of the species is recycled by decomposition as a new resource. First we consider an instantaneous model of Lotka-Volterra type, and prove that the positive equilibrium is always globally asymptotically stable with respect to R + 2 . Then we take account of the time delay in decomposition and in the assimilation of the nutrient. Using the Hopf bifurcation theorem we prove that the equilibrium can bifurcate from local stability to stable oscillation as the input of resource varies. These results are verified by computer simulations. The same qualitative behaviour arises if we substitute the uptake function of Lotka-Volterra type by a more realistic Michaelis-Menten function.

Keywords: Periodic Solution; Hopf Bifurcation; Local Stability; Positive Equilibrium; Stable Limit Cycle (search for similar items in EconPapers)
Date: 1988
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-009-2975-3_12

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DOI: 10.1007/978-94-009-2975-3_12

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