Criteria that forbid a large, nonlinear food-web model from having more than one equilibrium point

D. L. DeAngelis, R. A. Goldstein

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

Mathematical models of great complexity are being developed to help in understanding the behavior of ecosystems, but succinct conclusions for large models are difficult to obtain. In this report, criteria are introduced that guarantee that a given food-web model has no more than one equilibrium point. These criteria consist of biologically reasonable constraints on the behavior of the growth rates of the species as functions of population density plus the restriction of the food web to loops of lengths 1 and 2. While this last condition probably does not hold for most real food webs, the theorem may be robust enough to apply over a large range of cases. Authors analysis also suggests that increasing complexity in food-web models might be accompanied by a greater number of equilibrium points. Therefore, the chance of a system having at least one stable equilibrium point could increase as complexity increases, a conclusion of interest in the current debate over the relationship between stability and complexity.

Original languageEnglish
Pages (from-to)81-90
Number of pages10
JournalMathematical Biosciences
Volume41
Issue number1-2
DOIs
StatePublished - Sep 1 1978

Fingerprint

Food Web
Food Chain
Equilibrium Point
food webs
food web
Population Density
Ecosystem
Model
Ecosystems
population density
Theoretical Models
mathematical models
Mathematical Model
Mathematical models
Restriction
ecosystems
ecosystem
Growth
Theorem
Range of data

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)
  • Ecology, Evolution, Behavior and Systematics

Cite this

Criteria that forbid a large, nonlinear food-web model from having more than one equilibrium point. / DeAngelis, D. L.; Goldstein, R. A.

In: Mathematical Biosciences, Vol. 41, No. 1-2, 01.09.1978, p. 81-90.

Research output: Contribution to journalArticle

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