Limit Cycles in Competition Communities. Gilpin, M. E. The American Naturalist, 109(965):51--60, 1975. ArticleType: research-article / Full publication date: Jan. - Feb., 1975 / Copyright © 1975 The University of Chicago Press
Limit Cycles in Competition Communities [link]Paper  abstract   bibtex   
\textlessp\textgreaterA three-species Lotka-Volterra competition community may exhibit population oscillations of a neutral or undamped nature. Nontransitive interference competition, in which 1 can exclude 2, 2 can exclude 3, but 3 can exclude 1, is the underlying mechanism. If immigration, incomplete spatial overlap, or any other mechanism prevents extinction, then such a three-species system must go into true limit cycles. For higher-dimension systems, limit cycles are more likely in communities with an odd number of species. Such limit cycles are most likely to be found in the tropics. A cautionary moral is given: simple competition systems that appear to be unstable and random may be stable and deterministic.
@article{gilpin_limit_1975,
	title = {Limit {Cycles} in {Competition} {Communities}},
	volume = {109},
	issn = {0003-0147},
	url = {http://www.jstor.org/stable/2459636},
	abstract = {{\textless}p{\textgreater}A three-species Lotka-Volterra competition community may exhibit population oscillations of a neutral or undamped nature. Nontransitive interference competition, in which 1 can exclude 2, 2 can exclude 3, but 3 can exclude 1, is the underlying mechanism. If immigration, incomplete spatial overlap, or any other mechanism prevents extinction, then such a three-species system must go into true limit cycles. For higher-dimension systems, limit cycles are more likely in communities with an odd number of species. Such limit cycles are most likely to be found in the tropics. A cautionary moral is given: simple competition systems that appear to be unstable and random may be stable and deterministic.},
	number = {965},
	urldate = {2011-05-16TZ},
	journal = {The American Naturalist},
	author = {Gilpin, Michael E.},
	year = {1975},
	note = {ArticleType: research-article / Full publication date: Jan. - Feb., 1975 / Copyright © 1975 The University of Chicago Press},
	pages = {51--60}
}

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