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

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. This research is supported by the National Natural Science Foundation of China