一类具有交叉反应扩散的捕食-食饵模型的动态分歧  

Dynamic Bifurcation of a Class of Predator-Prey Models with Cross Reaction Diffusion

作　　者：亓子成 刘瑞宽 吴辰龙 QI Zicheng;LIU Ruikuan;WU Chenlong(School of Science,Southwest Petroleum University,Chengdu 610500,China)

机构地区：[1]西南石油大学理学院,成都610500

出　　处：《吉林大学学报（理学版）》2024年第5期1063-1071,共9页Journal of Jilin University:Science Edition

基　　金：四川省自然科学基金面上项目(批准号:20222NSFSC0529);南充市-西南石油大学市校科技战略合作专项基金(批准号:23XNSYJG0005)。

摘　　要：考虑一类具有Holling-Ⅱ型功能反应函数的交叉反应扩散模型在非齐次Dirichlet边界条件下的动态分歧问题.首先,用谱分析理论得到对应的线性化问题特征值的临界穿越条件;其次,选取环境承载系数为分歧参数,利用中心流形约化和动态分歧理论得到该系统的动态跃迁类型和分歧解的解析表达式.最后,利用有限差分法,在不同的参数情形下给出系统的斑图变化模式.We considered the dynamic bifurcation problem of a class of cross-reaction-diffusion models with Holling-Ⅱfunctional response function under non-homoge neous Dirichlet boundary conditions.Firstly,the critical crossing conditions for the corresponding linearization problem eigenvalues were obtained by using the spectral analysis theory.Secondly,the environmental carrying coefficient was selected as the bifurcation parameter,the analytical expression of the dynamic transition type and bifurcation solution of the system was obtained by using the center manifold reduction and the dynamic bifurcation theory.Finally,by using the finite difference method,the pattern change patterns of the system were given under different parameter conditions.

关 键 词：反应扩散模型 特征值分析 动态跃迁 数值模拟 

分 类 号：O175.29[理学—数学]