Abstract: The existence and stability of a predator-prey diffusive model with multiplicative Allee affect are discussed. The existence of bifurcating positive solutions is investigated by means of the local bifurcation theory. The stability of bifurcation solutions is determined. By using the global bifurcation theory, the local bifurcation is extended and the sufficiently conditions of the existence of positive solutions are obtained. The results indicate that the two species will coexist when the parameters satisfy certain conditions, furthermore the coexistence solutions are stable.

Key words: multiplicative Allee affect, bifurcation theory, stability

摘要： 讨论了一类带有乘法Allee效应的捕食-食饵扩散模型正解的存在性和稳定性。利用局部分歧理论研究了分歧正解的存在性，考察了分歧解的稳定性，运用全局分歧定理将局部分歧进行延拓从而得到了正解存在的充分条件。结果表明当参数满足一定条件时，两物种能共存而且共存解稳定。

关键词: 乘法Allee效应, 分歧理论, 稳定性