具时滞的捕食-食饵共生模型的Hopf分支  

Hopf Bifurcation of Predator-Prey Symbiotic Model with Time Delay

作　　者：高鹤 李秀玲[1] GAO He;LI Xiuling(School of Applied Mathematics,Jilin University of Finance and Economics,Changchun 130117,China)

机构地区：[1]吉林财经大学应用数学学院,长春130117

出　　处：《吉林大学学报（理学版）》2023年第6期1339-1350,共12页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:41301182);吉林省自然科学基金(批准号:20210101153JC)。

摘　　要：利用规范型理论和中心流形定理讨论具双时滞的捕食-食饵共生模型的Hopf分支.通过对特征方程的分析,以食饵的发育时间和共生者的发育时间作为分支参数,给出其平衡点的稳定性、Hopf分支的存在性以及分支方向和分支周期解的稳定性,得到了时滞会影响系统稳定性的结果,并通过数值模拟验证了所得结论的正确性.The Hopf bifurcation of predator-prey symbiotic model with double time delay was discussed by using the normal form theory and the central manifold theorem.By analyzing the characteristic equation and taking the development time of the prey and the development time of the co-genitor as the parameters,the stability of equilibrium point,the existence of Hopf bifurcation,the stability of bifurcation direction and bifurcating periodic solution were given.The result that time delay affected the stability of the system was obtained.The correctness of obtained conclusions was verified through numerical simulation.

关 键 词：HOPF分支 双时滞 捕食-食饵共生模型 

分 类 号：O193[理学—数学]