非均匀恒化器中具有抑制因子的食物链模型正解的存在性  

The existence of a positive solution of the food chain model with inhibitors in the unstirred chemostat

作　　者：成新宇 石垚 孙越 CHENG Xin-yu;SHI Yao;SUN Yue(School of Science,Chang'an University,Xi'an 710064,Shaanxi,China;Department of Ultrasound,Liaoyang City Central Hospital,Liaoyang 111000,Liaoning,China)

机构地区：[1]长安大学理学院,陕西西安710064 [2]辽阳市中心医院超声科,辽宁辽阳111000

出　　处：《西北师范大学学报(自然科学版)》2025年第2期117-124,共8页Journal of Northwest Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(12201067);中央高校基本科研业务费专项(300102124205,300102124201)。

摘　　要：研究了非均匀恒化器中具有抑制因子的高维食物链模型,其中两个竞争捕食者以生长在恒化器中的单个食饵为食.首先,运用特征值理论,得出系统正解存在的必要条件;然后,运用度理论和不动点指标等方法,给出具有抑制因子的食物链恒化器模型的正解;最后,通过数值模拟得到:食物链中食饵的最大生长率过大或过小都不利于多个物种的共存;对处于弱势的捕食者来说,抑制因子反而有助于其存活.A high-dimensional food chain model with inhibitors in an unstirred chemostat is studied in this paper,in which two competing predators feed on a single prey grown in the chemostat.Firstly,the eigenvalue theory is used to obtain the necessary conditions for the existence of the positive solution of the system.Then,using the degree theory and the fixed point index,the positive solution of the food chain chemostat model with inhibitors is given.Finally,through numerical simulation,it is found that the maximum growth rate of prey in the food chain is too large or too small,which is not conducive to the coexistence of multiple species.For predators who are in a vulnerable position,inhibitors can instead help them survive.

关 键 词：恒化器 抑制因子 食物链模型 度理论 特征值 正解 

分 类 号：O175.26[理学—数学]