一类分数阶比率依赖型捕食系统的动力学分析  

DYNAMICS OF A RATIO-DEPENDENT PREDATOR-PREY OF FRACTIONAL ORDER SYSTEM

作　　者：蒲武军[1] 杜争光[1] PU Wu-jun;DU Zheng-guang(Department of Mathematics,Longnan Teachers College,Longnan,Gansu 742500,China)

机构地区：[1]陇南师范高等专科学校数学系,甘肃陇南742500

出　　处：《井冈山大学学报（自然科学版）》2021年第2期14-18,共5页Journal of Jinggangshan University (Natural Science)

基　　金：陇南市2019年科技指导性计划项目(2019-ZD-14)。

摘　　要：讨论了一类食饵带有疾病的分数阶比率依赖型捕食系统的动力学行为。利用线性化方法定性分析了各类平衡点的稳定性,并给出了其正平衡点局部渐近稳定的充分条件。数值模拟显示,参数和阶数对平衡点的收敛速度及其稳定性产生很重要的影响。In this paper,we studied the dynamic behavior of a fractional-order ratio-dependent predator–prey system with disease on the prey.The stability of all kinds of equilibrium points of the system was qualitatively analyzed with the linearization method,the sufficient conditions for the local asymptotic stability of the positive equilibrium point of the system were given,and the numerical simulation showed that the parameters and order of the system had an important influence on the convergence rate and stability of the equilibrium point.

关 键 词：分数阶 比率依赖型捕食系统 局部渐近稳定性 HOPF分支 

分 类 号：O157.13[理学—数学]