具有记忆时滞的捕食者-食饵模型的分支分析  

BIFURCATION ANALYSIS OF A PREDATOR-PREY MODEL WITH MEMORY DELAY

作　　者：周鑫炎 王小利[1] ZHOU Xin-yan;WANG Xiao-li(School of Mathematics and Statistics,Southwest University,Chongqing 400715,China)

机构地区：[1]西南大学数学与统计学院,重庆400715

出　　处：《数学杂志》2024年第5期460-470,共11页Journal of Mathematics

摘　　要：本文研究了一类在Neumann边界条件下带有记忆时滞的捕食者-食饵模型稳定性以及分支的相关问题.利用强极大值原理和抛物方程的比较原理得到了模型的适定性(存在性、唯一性和正性),然后分析了系统中常数稳态解的稳定性;同时以基于记忆的扩散系数为分支参数,得到了系统的Turing分支和Hopf分支;说明了在该系统中对于任意的记忆时滞,总会存在大于临界值的记忆扩散系数,使得正常数稳态解是不稳定的;最后利用数值模拟验证相应结论.In this paper,we study the stability and bifurcation issues of a predator-prey model with memory delay under Neumann boundary conditions.The strong maximum principle and the comparison principle of parabolic equations are used to obtain the well-posedness of the model(existence,uniqueness and positivity),and then the stability of the constant steady-state solution in the system is analyzed.At the same time,the Turing bifurcation and Hopf bifurcation of the system are obtained by taking the memory-based di usion coecient as the bifurcation parameter;it is shown that for any memory delay in this system,there will always be a memory di usion coecient greater than the critical value,making the positive constant steady-state solution unstable.Finally,the numerical simulation is used to verify the corresponding conclusion.

关 键 词：反应-扩散方程 记忆时滞 适定性 Turing分支 HOPF分支 

分 类 号：O175[理学—数学]