一个带有交叉扩散的捕食-被捕食模型的动力学性质  

Dynamics of a Predator-prey Model with Cross Diffusion

作　　者：汪鹏飞[1] 于恒国 WANG Peng-fei YU Heng guo(School of Electro Mechanical and Information Technology, Yiwu Industrial and Commercial College ,Yiwu 322000,China College of Mathematics Information Science, Wenzhou University ,Wenzhou 325035,China)

机构地区：[1]义乌工商职业技术学院机电信息学院,浙江义乌322000 [2]温州大学数学与信息科学学院,浙江温州325035

出　　处：《滨州学院学报》2017年第2期38-44,共7页Journal of Binzhou University

基　　金：国家自然科学基金资助项目(31570364)

摘　　要：对一个带有自扩散和交叉扩散的捕食-被捕食模型进行研究,分析了该模型平衡点的局部以及全局稳定性,研究了当系统同时考虑自扩散和交叉扩散影响时稳定性的变化。证明了交叉扩散系数的变化对于该模型的局部和全局稳定性有重要的影响,并且证明了由交叉扩散导致的图灵失稳的多种情形。In this paper,apredator-prey model with self-diffusion and cross-diffusion is studied.The local and global stability of the system＇s equilibrium are studied,and the effects of self-diffusion and cross-diffusion on the stability are analyzed.The analysis shows that the cross-diffusion can play an important role in the local and global stability of the system.Furthermore,we found that the cross diffusion can cause the Turing instability in a variety of situations.

关 键 词：捕食-被捕食模型 交叉扩散 稳定性 图灵失稳 

分 类 号：O175[理学—数学]