食饵种群密度服从Gompertz增长率的时滞扩散捕食—食饵模型  

A Delayed Diffusive Predator-Prey Model with Prey Population Density Obeying Gompertz Growth Rate

作　　者：陈丹丹 陈金琼 张道祥 CHEN Dan-dan;CHEN Jin-qiong;ZHANG Dao-xiang(School of Mathematics and Statistics,Anhui Normal University,Wuhu 241002,China)

机构地区：[1]安徽师范大学数学与统计学院,安徽芜湖241002

出　　处：《安徽师范大学学报（自然科学版）》2021年第6期517-524,530,共9页Journal of Anhui Normal University(Natural Science)

基　　金：国家自然科学基金项目(12001011,11302002);安徽省自然科学基金项目(2008085MA13).

摘　　要：考虑食饵种群密度服从Gompertz增长率的时滞扩散捕食—食饵模型。首先,分析了系统正平衡点的存在性条件;其次,考虑了正平衡点的稳定性和Hopf分支存在的条件,同时讨论了时滞、扩散系数和食饵增长率对系统空间动力学的影响;最后,运用Matlab来模拟验证所做的工作。结果表明此系统具有丰富的动力学性态,如螺旋波斑图、混沌斑图。In this paper,we consider a delayed diffusive predator-prey model in which the prey population density obeys the Gompertz growth rate.Firstly,we analyze the existence conditions of the positive equilibrium point of the system.Secondly,we further consider the stability of the positive equilibrium point and the conditions for the existence of the Hopf bifurcation of the system.At the same time,the effects of time delay,diffusion coefficient and growth rate of prey on the space dynamics of the system are discussed.Finally,Matlab is used to simulate and verify the theoretical results.The results show that the system has rich dynamic characteristics,such as spiral wave pattern and chaotic pattern.

关 键 词：扩散捕食模型 时滞 Gompertz增长率 Hopf分支 斑图 

分 类 号：O175[理学—数学]