Resilience and local stability in a nutrient-limited resource-consumer system

H. Nakajima, D. L. DeAngelis

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

The "paradox of enrichment" predicts that increasing the growth rate of the resource in a resource-consumer dynamic system, by nutrient enrichment, for example, can lead to local instability of the system-that is, to a Hopf bifurcation. The approach to the Hopf bifurcation is accompanied by a decrease in resilience (rate of return to equilibrium). On the other hand, studies of nutrient cycling in food webs indicate that an increase in the nutrient input rate usually results in increased resilience. Here these two apparently conflicting theoretical results are reconciled with a model of a nutrient-limited resource-consumer system in which the tightly recycled limiting nutrient is explicitly modelled. It is shown that increasing nutrient input may at first lead to increased resilience and that resilience decreases sharply only immediately before the Hopf bifurcation is reached.

Original languageEnglish
Pages (from-to)501-510
Number of pages10
JournalBulletin of Mathematical Biology
Volume51
Issue number4
DOIs
StatePublished - Jul 1 1989

Fingerprint

Resilience
Local Stability
Nutrients
bifurcation
Food
Resources
Hopf bifurcation
nutrient
nutrients
resource
Hopf Bifurcation
nutrient enrichment
nutrient cycling
biogeochemical cycles
food webs
Food Web
food web
Decrease
Food Chain
Cycling

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)

Cite this

Resilience and local stability in a nutrient-limited resource-consumer system. / Nakajima, H.; DeAngelis, D. L.

In: Bulletin of Mathematical Biology, Vol. 51, No. 4, 01.07.1989, p. 501-510.

Research output: Contribution to journalArticle

Nakajima, H. ; DeAngelis, D. L. / Resilience and local stability in a nutrient-limited resource-consumer system. In: Bulletin of Mathematical Biology. 1989 ; Vol. 51, No. 4. pp. 501-510.
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