关键词: 乘法Allee效应, 分歧理论, 稳定性

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