This paper investigates the dynamics and optimal control of the Monod–Haldane predator–prey system with mixed harvesting that combines both continuous and impulsive harvestings. The periodic solution of the prey-free is studied and the local stability condition is obtained. The boundedness of solutions, the permanence of the system, and the existence of nontrivial periodic solution are studied. With the change of parameters, the system appears with a stable nontrivial periodic solution when the prey-free periodic solution loses stability. Numerical simulations show that the system has complex dynamical behaviors via bifurcation diagrams. Further, the maximum yield problem of the harvested system is studied, which is transformed into a nonlinear programming problem and solved by the method of combined multiple shooting and collocation.

中文翻译：

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Monod-Haldane 捕食者-猎物混合捕食系统的动力学与优化控制

本文研究了 Monod-Haldane 捕食者 - 猎物系统的动态和优化控制，该系统采用混合捕捞方式，结合了连续捕捞和脉冲捕捞。研究了无猎物的周期解，得到了局部稳定条件。研究了解的有界性、系统的持久性和非平凡周期解的存在性。随着参数的变化，当无猎物周期解失去稳定性时，系统出现稳定的非平凡周期解。数值模拟表明，系统通过分岔图具有复杂的动力学行为。进一步研究了收获系统的最大产量问题，将其转化为非线性规划问题，采用多拍搭配组合的方法求解。