具有非线性交叉扩散的Lotka-Volterra竞争系统的共存解  

Coexistence Solutions of Lotka-Volterra Competitive Systems with Nonlinear Cross Diffusion

作　　者：贺子鹏 董亚莹 HE Zipeng;DONG Yaying(School of Science,Xi’an Polytechnic University,Xi’an 710048,China)

机构地区：[1]西安工程大学理学院,西安710048

出　　处：《吉林大学学报（理学版）》2023年第3期459-468,共10页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11801431);陕西省高校科协青年人才托举计划项目(批准号:20190509);陕西省自然科学基金一般项目(面上)(批准号:2023-JC-YB-038).

摘　　要：考虑一类齐次Dirichlet边界条件下具有非线性交叉扩散的Lotka-Volterra竞争系统的共存解问题.首先,借助线性算子的谱理论分析该问题平凡解和半平凡解的稳定性;其次,利用正锥上的不动点指数理论给出该问题共存解存在的充分条件.We considered the coexistence solution problem of a class of Lotka-Volterra competitive systems with nonlinear cross-diffusion under homogeneous Dirichlet boundary conditions.Firstly,the stability of trivial solutions and semi-trivial solutions of the problem was analyzed by using spectral theory of linear operators.Secondly,sufficient conditions for the existence of coexistence solutions of the problem were given by using the fixed point index theory on positive cone.

关 键 词：竞争模型 交叉扩散 稳定性 不动点指数 共存解 

分 类 号：O175.26[理学—数学]