具有抑制因子的食物链恒化器模型的正解研究
Positive Solution Study of the Food Chain Chemostat Model with Inhibitors
DOI: 10.12677/aam.2026.154193, PDF,    国家自然科学基金支持
作者: 成新宇：长安大学理学院，陕西 西安
关键词: 恒化器；抑制因子；捕食食饵模型；Chemostat； Inhibitor； Predator-Prey Model
摘要: 本文研究了非均匀恒化器中具有抑制因子的食物链模型，其中捕食者以生长在恒化器中的单个食饵为食，总体捕食者对可育捕食者存在抑制作用。首先，运用线性化特征值理论，得出系统平凡解和半平凡解的稳定性；然后，运用分歧理论等研究了模型的正稳态解分支，局部分歧解的稳定性以及将局部分歧延拓为全局分歧。
Abstract: In this paper, a predator-prey model with inhibitors in an unstirred chemostat is studied, in which the predator feeds on a single prey growing in the chemostat, and the overall predator has an inhibitory effect on reproducing predators. Firstly, the linearization eigenvalue theory is used to obtain the stability of the trivial and semi-trivial solutions of the system. Then, using bifurcation theory and other methods, the branches of the model’s positive steady-state solutions, the stability of local bifurcation solutions, and the continuation of local bifurcations to global bifurcations were studied.
文章引用：成新宇. 具有抑制因子的食物链恒化器模型的正解研究[J]. 应用数学进展, 2026, 15(4): 680-693. https://doi.org/10.12677/aam.2026.154193

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