一类具有Smith增长率和B-D功能反应的时滞反应扩散捕食系统的动力学分析  

Dynamics Analysis of a Delayed Reaction-Diffusion Predator-Prey System with Smith Growth Rate and B-D Functional Response

作　　者：焦建锋 常红翠 陈灿 罗敏 JIAO Jian-feng;CHANG Hong-cui;CHEN Can;LUO Min(School of Mathematics,Zhengzhou University of Aeronautics,Zhengzhou 450046,China;School of Economics,Zhengzhou University of Aeronautics,Zhengzhou 450046,China;School of Science,Hangzhou Dianzi University,Hangzhou 310018,China)

机构地区：[1]郑州航空工业管理学院数学学院,河南郑州450046 [2]郑州航空工业管理学院经济学院,河南郑州450046 [3]杭州电子科技大学理学院,浙江杭州310018

出　　处：《数学的实践与认识》2024年第8期184-190,共7页Mathematics in Practice and Theory

基　　金：河南省自然科学基金(242300421696);国家自然科学基金(12201163);河南省高等学校重点科研项目计划基础研究专项(24ZX008);浙江省自然科学基金(LQ23A010016)。

摘　　要：主要研究了一类具有Smith增长率和B-D功能反应函数的时滞反应扩散捕食系统的稳定性分析问题.首先,计算了常微分系统平衡点的存在条件和稳定条件,并给出了对应的数值模拟结果.其次,利用泰勒展开将时滞反应扩散系统转化为反应扩散系统,并通过特征根分析法,得到了系统在正平衡点处发生Turing分支的参数空间.最后,我们给出了系统发生Turing分支的数值模拟,并分析了时滞参数τ和交叉扩散系数对系统动力学行为的影响.这些理论结果将为种群间调控关系的理解提供重要帮助.This paper mainly studies the stability analysis of a class of delayed reactiondiffusion predator-prey systems with Smith growth rate and B-D functional response function.Firstly,we calculate the existence and stability conditions of equilibrium for the ordinary differential system,and provide corresponding numerical simulation results.Secondly,we use Taylor expansion to transform the delayed reaction-diffusion system into a reaction-diffusion system,and obtain the parameter space where the system undergoes Turing bifurcation at the positive equilibrium through eigenvalue analysis.Finally,we provide numerical simulations of the system undergoing Turing bifurcation,and analyze the effects of delay parameterτand cross-diffusion coefficient on the dynamical behavior of the system.These theoretical results will provide important help for understanding the regulatory relationship between populations.

关 键 词：时滞 反应扩散方程 Smith增长率 B-D功能反应 图灵分支 

分 类 号：Q141[生物学—生态学] O175[生物学—普通生物学]