Periodic Lotka-Volterra competition equations

J. M. Cushing

Research output: Contribution to journalArticlepeer-review

43 Scopus citations


The Lotka-Volterra competition equations with periodic coefficients derived from the MacArthur-Levins theory of a one-dimensional resource niche are studied when the parameters are allowed to oscillate periodically in time. Specifically, niche positions and widths, resource availability and resource consumption rates are allowed small amplitude periodicities around a specified mean value. Two opposite cases are studied both analytically and numerically. First only resource consumption rates are allowed to oscillate while niche dimensions and resource availability are held constant. The resulting oscillations in population densities and the strength of the system stability as they depend upon crucial relative phase and amplitude differences between the species' consumption rates are studied. This leads to a clear notion of "temporal niche" and of the effects that such oscillations can have on competitive coexistence. Secondly, all system parameters are allowed to oscillate, although the oscillatory consumption rates are assumed identical for both species. The effects on the population density oscillations and their averages are studied and the "best" choice of the common, periodic resource consumption rate for these two "identical" species competing for similar (even identical) niches is considered.

Original languageEnglish (US)
Pages (from-to)381-403
Number of pages23
JournalJournal of mathematical biology
Issue number4
StatePublished - Jul 1986


  • Lotka-Volterra competition
  • MacArthur-Levins theory
  • Periodic coefficients
  • Temporal niche

ASJC Scopus subject areas

  • Modeling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics


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