We investigate a diffusive predator–prey system with discontinuous harvesting function under Neumann boundary conditions. Then the existence and some estimates of the positive solution of the system are acquired. Based on the differential inclusions theory, we discuss the existence of constant equilibrium. Finally, by constructing a suitable Lyapunov functional, we study the global asymptotic stability of the positive equilibrium.

中文翻译：

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具有不连续收获策略的扩散捕食模型的全局稳定性

我们研究了在诺伊曼边界条件下具有不连续收获功能的扩散捕食－被捕食系统。然后获得系统正解的存在性和估计。基于微分包含理论，我们讨论了常数平衡的存在。最后，通过构造合适的Lyapunov泛函，我们研究了正平衡的全局渐近稳定性。