一类时滞捕食-食饵系统的全局Hopf分支  

Global Hopf bifurcation for a delayed apredator-prey systems

作　　者：王麟 Wang Lin(School of Science,Heilongjiang University of Science&Technology,Harbin 150022,China)

机构地区：[1]黑龙江科技大学理学院,哈尔滨150022

出　　处：《黑龙江科技大学学报》2024年第3期481-486,共6页Journal of Heilongjiang University of Science And Technology

摘　　要：为了解决种群动力学模型周期解的整体存在性问题,以一类时滞捕食-食饵模型为研究对象,通过选择时滞τ作为分支参数,研究正平衡点的稳定性和Hopf分支问题。结果表明:当τ穿过某些临界值时,系统在正平衡点附近会发生局部Hopf分支;利用中心流形定理和规范型理论,得到Hopf分支的方向和分支周期解的稳定性算法,根据拓扑度理论证明了全局Hopf分支的存在性。This paper aims to solve the global existence problem of periodic solutions for population dynamics models.The study taking a kind of time delayed predator-prey model as the subject,chooses the delayτas a bifurcation parameter,and studies the stability of positive equilibrium and Hopf bifurcation.The research shows that the local Hopf bifurcation can occur in system near the positive equilibrium point asτcrosses some critical values.The direction of the Hopf bifurcation and the stability of the bifurcation periodic solutions can be determined by using the central manifold and normal form theory.The existence of global Hopf bifurcation is proved based on topological theory.

关 键 词：捕食-食饵模型 时滞 HOPF分支 

分 类 号：O175.1[理学—数学]