具有恐惧效应和半封闭捕获的Holling-Ⅱ类时滞捕食系统Hopf分岔

Hopf Bifurcation of a Delayed Holling-II Predator-prey System with Fear Effect and Partial Closure for the Populations

研究一类具有恐惧效应和半封闭捕获的Holling-Ⅱ类时滞捕食系统。以捕食者的妊娠时滞为分岔参数,推导出系统正平衡点的局部渐近稳定性和产生Hopf分岔的充分条件。最后,给出仿真示例验证所得结果的正确性,以及食饵种群和捕食者种群可供捕捞的比例对系统的影响。

A delayed Holling-II predator-prey system is studied with fear effect and partial closure for the populations.Sufficient conditions for the local asymptotic stability of the positive equilibrium and exhibition of the Hopf bifurcation are derived by taking gestation delay of the predator as bifurcation parameter.Finally,a simulation example is given to verify the correctness of the results and the impact of the available proportion of the prey and predator for fishing in the system.