中文摘要：

讨论了一类带有保护区域和加法Allee效应的扩散捕食-食饵模型。首先讨论了平凡解和半平凡解的稳定性,接着考察了非常数正解的不存在性,最后运用全局分歧理论得到了非常数正解的存在性条件。研究结果表明,在弱Allee效应下,当扩散系数适当且参数满足一定条件时,两物种能共存而且共存解稳定;当扩散系数充分大时两物种不共存。

英文摘要：

A diffusive predator-prey model with additive Allee effect and a protection zone is discussed. Firstly,the stability of trivial and semi-trivial solutions is investigated. Secondly,the non-existence of non-constant positive solutions is determined. Finally,the existence of non-constant positive solutions is obtained by using the global bifurcation theory. Under weakly Allee effect,the results indicate that the two species will coexist and the coexistence solutions are stable when the diffusion coefficient is suitably chosen and the parameters satisfy certain conditions. Furthermore,the two species cannot coexist when the diffusion coefficients are sufficiently large.