In this paper, a Gause type predator–prey system with constant-yield prey harvesting and monotone ascending functional response is proposed and investigated. We focus on the influence of the harvesting rate on the predator–prey system. First, equilibria corresponding to different situations are investigated, as well as the stability analysis. Then bifurcations are explored at nonhyperbolic equilibria, and we give the conditions for the occurrence of two saddle–node bifurcations by analyzing the emergence, coincidence and annihilation of equilibria. We calculate the Lyapunov number and focal values to determine the stability and the quantity of limit cycles generated by supercritical, subcritical and degenerate Hopf bifurcations. Furthermore, the system is unfolded to explore the repelling and attracting Bogdanov–Takens bifurcations by perturbing two bifurcation parameters near the cusp. It is shown that there exists one limit cycle, or one homoclinic loop, or two limit cycles for different parameter values. Therefore, the system is susceptible to both the constant-yield prey harvesting and initial values of the species. Finally, we run numerical simulations to verify the theoretical analysis.

在本文中，提出并研究了具有恒定产量猎物收获和单调上升功能响应的Gause型捕食者-猎物系统。我们关注捕食率对捕食者-猎物系统的影响。首先，研究了对应于不同情况的平衡，以及稳定性分析。然后在非双曲平衡处探索分岔，通过分析平衡的出现、重合和湮灭，我们给出了两个鞍点分岔发生的条件。我们计算李雅普诺夫数和焦点值，以确定稳定性和超临界、亚临界和简并 Hopf 分岔产生的极限循环的数量。此外，该系统展开以通过扰动尖端附近的两个分岔参数来探索排斥和吸引 Bogdanov-Takens 分岔。结果表明，对于不同的参数值，存在一个极限环，或一个同宿环，或两个极限环。因此，该系统易受恒定产量猎物收获和物种初始值的影响。最后，我们运行数值模拟来验证理论分析。