A single species stage structure model with Michaelis–Menten-type juvenile population harvesting is proposed and investigated. The existence and local stability of the model equilibria are studied. It shows that for the model, two cases of bistability may exist. Some conditions for the global asymptotic stability of the boundary equilibrium are derived by constructing some suitable Lyapunov functions. After that, based on the Bendixson–Dulac discriminant, we obtain the sufficient conditions for the global asymptotic stability of the internal equilibrium. Our study shows that nonlinear harvesting can make the dynamics of the system more complex than linear harvesting; for example, the system may admit the bistable stability property. Numeric simulations support our theoretical results.

中文翻译：

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具有Michaelis–Menten型少年种群收获的单物种阶段结构模型的动力学行为

提出并研究了具有Michaelis–Menten型少年种群收获的单物种阶段结构模型。研究了模型平衡的存在性和局部稳定性。它表明，对于该模型，可能存在两种双稳态情况。通过构造一些合适的Lyapunov函数，得出边界平衡的全局渐近稳定性的一些条件。之后，根据本迪克森-杜拉克判别式，我们获得了内部均衡的全局渐近稳定性的充分条件。我们的研究表明，非线性收获比线性收获可以使系统的动力学更加复杂。例如，系统可以接受双稳态稳定性能。数值模拟支持我们的理论结果。