This paper is concerned with a prey–predator model with population flux by attractive transition. Our previous paper (Oeda and Kuto, 2018, Nonlinear Anal. RWA, 44, 589–615) obtained a bifurcation branch (connected set) of coexistence steady states which connects two semitrivial solutions. In Oeda and Kuto (2018, Nonlinear Anal. RWA, 44, 589–615), we also showed that any positive steady-state approaches a positive solution of either of two limiting systems, and moreover, one of the limiting systems is an equal diffusive competition model. This paper obtains the bifurcation structure of positive solutions to the other limiting system. Moreover, this paper implies that the global bifurcation branch of coexistence states consists of two parts, one of which is a simple curve running in a tubular domain near the set of positive solutions to the equal diffusive competition model, the other of which is a connected set characterized by positive solutions to the other limiting system.

本文关注具有吸引力转变的种群通量的猎物 - 捕食者模型。我们之前的论文 (Oeda and Kuto, 2018, Nonlinear Anal. RWA , 44, 589–615) 获得了连接两个半平凡解的共存稳态的分岔分支（连通集）。在 Oeda 和 Kuto (2018, Nonlinear Anal. RWA, 44, 589-615)，我们还表明，任何正稳态都接近两个限制系统中的任何一个的正解，此外，其中一个限制系统是等扩散竞争模型。本文得到了另一个极限系统正解的分岔结构。此外，本文暗示共存状态的全局分岔分支由两部分组成，其中一部分是在等扩散竞争模型的正解集附近的管状域中运行的简单曲线，另一部分是连通的以对另一个限制系统的正解为特征的集合。