Limit Cycles in Predator-Prey Communities

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Science  08 Sep 1972:
Vol. 177, Issue 4052, pp. 900-902
DOI: 10.1126/science.177.4052.900


Essentially all models that have been proposed for predator-prey systems are shown to possess either a stable point equilibrium or a stable limit cycle. This stable limit cycle, an explicitly nonlinear feature, is commonly overlooked in conventional analyses of these models. Such a stable limit cycle provides a satisfying explanation for those animal communities in which populations are observed to oscillate in a rather reproducible periodic manner.