空间同宿环和异宿环的稳定性

关于平面同（异）宿环的稳定性已有不少文献讨论过，但关于空间同（异）宿环的稳定性尚没有任何结果．本文在可定义回复映射的条件下给出了同（异）宿环在其部分邻域中是渐近稳定的判据．这些结果在某种意义下是平面系统相应结果的推广，包括并推广了［２］，［３］的结果．本文最后讨论了Ｌｏｒｅｎｚ系统同宿环和三种群竞争系统异宿环的稳定性，所得结果和Ｓｐａｒｒｏｗ与Ｍａｙ等的数值结果相吻合．

On the Stability of a Homoclinic Cycle and a Heterocliulc Cycle in Space

After defining the concept of stability of a homoclinic cycle or a heteroclinic cycle in their part neighborhood for space systems,this paper gives a criterion for determining the stability of a homoclinic cycle or a heteroclinic cycle in space for the fast time.The results given in this paper include and extend the results already obtained by the authors of 1]-3] which are used to determine the stability of a homoclinic cycle or a heteroclinic cycle on a plane in a sense.Lastly the stability of the homoclinic cycle in Lorenz system and the stability of the heteroclinic cycle in a ecological model with 3-species by Lotka-Volterra equation are discussed.The result obtained coinsides with the conclusion of.9]-11].