A strategic model of material cycling in a closed ecosystem

R.M.  Nisbet; J. McKinstry; William Gurney

doi:10.1016/0025-5564(83)90030-5

A strategic model of material cycling in a closed ecosystem

R.M. Nisbet, J. McKinstry, William Gurney

Mathematics And Statistics

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Abstract

The aim of this paper is to reconcile the observed vulnerability of self-sustaining (materially closed) experimental ecosystems with demonstrations of virtually unconditional stability in mathematical models incorporating material recycling. We prove deterministic local stability in a generalized version of a model previously investigated by two of us (Nisbet and Gurney), but show that, except with rather narrowly specified parameter values, the system is likely to be extremely sensitive to external perturbations.

Original language	English
Pages (from-to)	99-113
Number of pages	15
Journal	Mathematical Biosciences
Volume	64
Issue number	1
DOIs	https://doi.org/10.1016/0025-5564(83)90030-5
Publication status	Published - May 1983

Keywords

experimental ecosystems
unconditional stability
local stability

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abstract = "The aim of this paper is to reconcile the observed vulnerability of self-sustaining (materially closed) experimental ecosystems with demonstrations of virtually unconditional stability in mathematical models incorporating material recycling. We prove deterministic local stability in a generalized version of a model previously investigated by two of us (Nisbet and Gurney), but show that, except with rather narrowly specified parameter values, the system is likely to be extremely sensitive to external perturbations.",

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AB - The aim of this paper is to reconcile the observed vulnerability of self-sustaining (materially closed) experimental ecosystems with demonstrations of virtually unconditional stability in mathematical models incorporating material recycling. We prove deterministic local stability in a generalized version of a model previously investigated by two of us (Nisbet and Gurney), but show that, except with rather narrowly specified parameter values, the system is likely to be extremely sensitive to external perturbations.

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KW - unconditional stability

KW - local stability

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