We propose and study a Lotka–Volterra predator–prey system incorporating both Michaelis–Menten-type prey harvesting and fear effect. By qualitative analysis of the eigenvalues of the Jacobian matrix we study the stability of equilibrium states. By applying the differential inequality theory we obtain sufficient conditions that ensure the global attractivity of the trivial equilibrium. By applying Dulac criterion we obtain sufficient conditions that ensure the global asymptotic stability of the positive equilibrium. Our study indicates that the catchability coefficient plays a crucial role on the dynamic behavior of the system; for example, the catchability coefficient is the Hopf bifurcation parameter. Furthermore, for our model in which harvesting is of Michaelis–Menten type, the catchability coefficient is within a certain range; increasing the capture rate does not change the final number of prey population, but reduces the predator population. Meanwhile, the fear effect of the prey species has no influence on the dynamic behavior of the system, but it can affect the time when the number of prey species reaches stability. Numeric simulations support our findings.

我们提出并研究了结合了米利斯-门腾型猎物的收获和恐惧效应的洛特卡-沃尔泰拉捕食者-猎物系统。通过对雅可比矩阵特征值的定性分析，我们研究了平衡态的稳定性。通过应用微分不等式理论，我们获得了确保微不足道的平衡的全局吸引性的充分条件。通过应用Dulac准则，我们获得了确保正平衡的全局渐近稳定性的充分条件。我们的研究表明，可捕获性系数对系统的动态行为起着至关重要的作用。例如，可捕获性系数是Hopf分支参数。此外，对于我们的米氏（Michaelis–Menten）类型的收获模型，可捕性系数在一定范围内；增加捕获率不会改变捕食者的最终数量，但会减少捕食者的数量。同时，猎物种类的恐惧效应对系统的动态行为没有影响，但是会影响猎物种类达到稳定状态的时间。数值模拟支持我们的发现。