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Oscillations of a Biotic Species Feeding on an Abiotic Resource

In: Biomathematics and Related Computational Problems

Author

Listed:
  • 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)

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.

Suggested Citation

  • E. Beretta & G. I. Bischi & F. Solimano, 1988. "Oscillations of a Biotic Species Feeding on an Abiotic Resource," Springer Books, in: Luigi M. Ricciardi (ed.), Biomathematics and Related Computational Problems, pages 121-131, Springer.
    • Handle: RePEc:spr:sprchp:978-94-009-2975-3_12
    DOI: 10.1007/978-94-009-2975-3_12
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