二维具时滞捕食-食饵共生模型的Hopf分支

Hopf bifurcation of a two-dimensionalpredator-prey symbiosis model with time delay

利用规范型理论和中心流形定理研究了一类二维具时滞的捕食-食饵共生模型的Hopf分支.通过对特征方程的分析,给出了其平衡点的稳定性、Hopf分支的存在性以及分支方向和分支周期解的稳定性等结果,并通过数值模拟验证了所得结论的正确性.

The Hopf bifurcation of a two-dimensional predator-prey symbiotic model with time delay is studied using the canonical form theory and the central manifold theorem.By analyzing the characteristic equation,the stability of equilibrium point,the existence of Hopf bifurcation,the stability of bifurcation direction and bifurcation periodic solution are given,and the correctness of the conclusions is verified by numerical simulation.