具有收获和阶段结构的比率依赖的捕食系统

A ratio-dependent predator system with a stage structure and harvesting

研究了具有收获和时滞,且捕食者具有阶段结构的比率依赖的捕食系统.以时滞τ为分支参数,运用Hopf分支理论,在一定条件下,得到当时滞τ<τ_0时正平衡点是局部渐近稳定的,当时滞τ<τ_0时正平衡点是不稳定的,即当τ经过临界值τ_0时系统出现Hopf分支.用Matlab软件进行数值仿真验证了结论的正确性.

A ratio-dependent predator system with a stage structure for the predator, time delay and harvesting was investigated. By means of the Hopf bifurcation theorem and consideration of the delay r as a bifurcation parameter, the endemic equilibrium was locally stable when ττ0, and unstable when ττ0,which meant Hopf bifurcation occurred when r passed through the critical values τ0. Matlab was employed to carry out numerical simulation to verify our results.