具线性收获率的时滞捕食系统的稳定性与Hopf分岔

Stability and Hopf bifurcation of a delayed prey system with linear harvesting rate

研究了一类具有线性收获率和时滞的捕食-被捕食模型,通过分析该系统在正平衡点的线性化方程,得到了正平衡点局部稳定的条件,进而得到出现Hopf分岔的条件。通过应用规范型理论和中心流形定理,得到了确定Hopf分岔方向和分岔周期解的稳定性计算公式。最后,利用数值模拟验证了研究结果。

A delayed predator-prey model with linear harvesting rate is proposed.By analyzing the linearizing system at the positive equilibrium,the local stability of positive equilibrium as well as the existence of Hopf bifurcation are studied.Based on the normal form theory and center manifold theorem for Hopf bifurcation,the direction of Hopf bifurcation is determined and the stability of bifurcating periodic solutions is obtained.Finally,numerical simulations are carried out to illustrate the theoretical results.