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
王麟1
作者信息
- 1. 黑龙江科技大学 理学院,哈尔滨 150022
- 折叠
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.
Abstract
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 delay τ as a bifurcation parameter,and studies the stability of positive equilibrium and Hopf bifurca-tion.The research shows that the local Hopf bifurcation can occur in system near the positive equilibrium point as τ crosses some critical values.The direction of the Hopf bifurcation and the stability of the bifur-cation periodic solutions can be determined by using the central manifold and normal form theory.The ex-istence of global Hopf bifurcation is proved based on topological theory.
关键词
捕食-食饵模型/时滞/Hopf分支Key words
predator-prey model/time delay/Hopf bifurcation引用本文复制引用
出版年
2024
国家科技期刊平台
NSTL
万方数据