Two species competition in a periodic environment

Research output: Contribution to journalArticle

116 Citations (Scopus)

Abstract

The classical Lotka-Volterra equations for two competing species have constant coefficients. In this paper these equations are studied under the assumption that the coefficients are periodic functions of a common period. As a generalization of the existence theory for equilibria in the constant coefficient case, it is shown that there exists a branch of positive periodic solutions which connects (i.e. bifurcates from) the two nontrivial periodic solutions lying on the coordinate axes. This branch exists for a finite interval or "spectrum" of bifurcation parameter values (the bifurcation parameter being the average of the net inherent growth rate of one species). The stability of these periodic solutions is studied and is related to the theory of competitive exclusion. A specific example of independent ecological interest is examined by means of which it is shown under what circumstances two species, which could not coexist in a constant environment, can coexist in a limit cycle fashion when subjected to suitable periodic harvesting or removal rates.

Original languageEnglish (US)
Pages (from-to)385-400
Number of pages16
JournalJournal of Mathematical Biology
Volume10
Issue number4
DOIs
StatePublished - 1980

Fingerprint

equilibrium theory
competitive exclusion
Periodic Solution
Branch
Coefficient
Bifurcation
Growth
Lotka-Volterra Equations
Competitive Exclusion
Competing Species
Existence Theory
Co-ordinate axis
Positive Periodic Solution
Harvesting
Periodic Functions
Limit Cycle
Interval
Generalization

Keywords

  • Bifurcation
  • Competition
  • Competitive exclusion
  • Periodic environment

ASJC Scopus subject areas

  • Agricultural and Biological Sciences (miscellaneous)
  • Mathematics (miscellaneous)

Cite this

Two species competition in a periodic environment. / Cushing, Jim M.

In: Journal of Mathematical Biology, Vol. 10, No. 4, 1980, p. 385-400.

Research output: Contribution to journalArticle

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