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The heteroclinic cycle in the model of competition betweenn species and its stability

Research paper by Feng Beiye

Indexed on: 01 Oct '98Published on: 01 Oct '98Published in: Acta Mathematicae Applicatae Sinica, English Series



Abstract

This paper gives a sufficient condition for the existence of heteroclinic cycle in the model of competition betweenn species and a criterion for determining the stability of the heteroclinic cycle. The results given in this paper extend the results obtained by May and Leonard in and by Hofbauer and Sigmund in. A conjecture on the permanence of the model and a open problem on the stability of the heteroclinic cycle for the critical case are given at the end of this paper.