具有食饵趋向性的捕食-食饵系统的正稳态解  

Positive steady-state solutions of a predator-preysystem with prey-taxis

作　　者：董亚莹 高歌 DONG Yaying;GAO Ge(Scchool of Science,Xi’an Polytechnic University,Xi’an 710048,China)

机构地区：[1]西安工程大学理学院,陕西西安710048

出　　处：《西安工程大学学报》2024年第4期122-132,共11页Journal of Xi’an Polytechnic University

基　　金：国家自然科学基金(11801431);陕西省高校科协青年人才托举计划(20190509);陕西省自然科学基金面上项目(2023-JC-YB-038,2024JC-YBMS-001)。

摘　　要：本文考虑了一类在齐次Dirichlet边界条件下具有食饵趋向性的捕食-食饵模型。基于模型正解的先验估计,利用线性化算子的特征值理论以及谱理论,得到了平凡解与半平凡解的渐近稳定性,运用正锥中的不动点指数理论,建立了正稳态解的存在性。通过对2个相关特征值的分析,进一步得到了模型正解关于2个物种增长率的共存区域。研究结果表明:食饵趋向性对模型的稳态解具有明显影响。A predator-prey model with prey-taxis under homogeneous Dirichlet boundary conditions was established.Based on the prior estimate of positive solutions,the asymptotic stability of trivial and semi-trivial solutions was obtained by using the eigenvalue theory of linearization operators and spectral theory.The existence of positive steady-state solutions was established using the fixed point index theory in a cone.By analyzing two related eigenvalues,the coexistence region with respect to the growth rates of two species was obtained.The results show that prey-taxis has an obvious influence on the steady-state solutions.

关 键 词：捕食-食饵系统 食饵趋向 稳定性 正稳态解 

分 类 号：O175.26[理学—数学]