摘要
考虑一类具有恐惧效应的时滞捕食者-食饵模型.先利用特征方程和Lyapunov-LaSalle不变性原理,证明当R(τ)≤1时边界平衡点的全局渐近稳定性;再利用时滞微分方程Hopf分支理论,讨论当R(τ)>1时共存平衡点的稳定性和全局Hopf分支的存在性,得到了恐惧效应与时滞会影响系统稳定性的结果;最后通过数值模拟验证理论结果的正确性.
The author considered a class of delayed predator-prey model with fear effect.Firstly,by using the characteristic equation and Lyapunov-LaSalle invariance principle,the global asymptotic stability of the boundary equilibrium was proved when R(τ)≤1.Secondly,by using the Hopf bifurcation theory of delay differential equation,the author discussed the stability of the coexistence equilibrium point and the existence of the global Hopf bifurcation when R(τ)>1,and obtained the results that fear effect and delay affected the stability of the system.Finally,the correctness of the theoretical results was verified by numerical simulations.
作者
王灵芝
WANG Lingzhi(School of Mathematics and Statistics,Shaanxi Normal University,Xi’an 710119,China)
出处
《吉林大学学报（理学版）》
CAS
北大核心
2023年第3期449-458,共10页
Journal of Jilin University:Science Edition
基金
国家自然科学基金(批准号:11971285).
