摘要
以时滞τ为分支参数,通过分析特征方程,给出时滞对正平衡点稳定性的影响以及Hopf分支产生的条件。利用规范型理论和中心流形定理,得到Hopf分支方向和周期解稳定性的判定条件。最后借助数值模拟验证理论结果。
Taking the time delayτas the bifurcation parameter,the effect of time delay on the stability of the positive steady state point and the existence of Hopf bifurcation are given by analyzing the characteristic equation.The criteria for the direction of Hopf bifurcation and the stability of periodic solutions are obtained by the normal form theory and the center manifold theorem.Finally,the theoretical results are verified by numerical simulations.
作者
郭改慧
王晶晶
李旺瑞
Gaihui GUO;Jingjing WANG;Wangrui LI(School of Mathematics and Data Science,Shaanxi University of Science and Technology,Xi'an 710021,Shaanxi,China)
出处
《山东大学学报（理学版）》
CAS
CSCD
北大核心
2023年第10期32-42,53,共12页
Journal of Shandong University(Natural Science)
基金
国家自然科学基金资助项目(61872227,12126420)
关键词
植被-水模型
时滞
HOPF分支
稳定性
vegetation-water model
time delay
Hopf bifurcation
stability
