一类具有密度制约的时滞捕食与被捕食系统解的稳定性分析  

Analysis on the Stability of Solutions for a Predator-prey System with Delay and Density Constraints

作　　者：方辉平 Fang Huiping(School of Mathematics and Statistics,Huangshan University,Huangshan 245041,China)

机构地区：[1]黄山学院数学与统计学院,安徽黄山245041

出　　处：《黄山学院学报》2020年第5期1-3,共3页Journal of Huangshan University

基　　金：国家自然科学基金(11701208);安徽省优秀人才基金重点项目(gxyqZD2016300);安徽省级教学团队(jxtd150)。

摘　　要：时滞是生态系统中一种普遍现象,两种群的相互时滞影响更加丰富了动力学行为。针对一类具有双时滞的捕食与被捕食模型,首先对系统进行线性化,根据系数矩阵的两个对角线乘积的关系,分析时滞参数变化引起特征方程纯虚根的变化,再利用非线性动力系统的稳定性理论,系统地讨论零解的稳定性。Delay is a common phenomenon in ecosystem.The interaction of two populations with delay leads to more abundant dynamic behaviors.In this paper,a predator-prey model with two delays is linearized firstly,and according to the relationship between the two diagonal products of the coefficient matrix,the change of the pure virtual root of the characteristic equation caused by the delay parameters is analyzed.With the stability theory of the nonlinear dynamic system,the stability of the zero solution is systematically discussed.

关 键 词：时滞 特征方程 稳定性 捕食与被捕食模型 

分 类 号：O175.12[理学—数学]