This paper is devoted to the dynamics of a predator-prey model with stage structure for prey and state-dependent maturation delay. Firstly, positivity and boundedness of solutions are addressed to describe the population survival and the natural restriction of limited resources. Secondly, the existence, uniqueness, and local asymptotical stability of (boundary and coexisting) equilibria are investigated by means of degree theory and Routh-Hurwitz criteria. Thirdly, the explicit bounds for the eventual behaviors of the mature population are obtained. Finally, by means of comparison principle and two auxiliary systems, it observed that the local asymptotical stability of either of the positive interior equilibrium and the positive boundary equilibrium implies that it is also globally asymptotical stable if the derivative of the delay function around this equilibrium is small enough.

中文翻译：

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具有状态依赖时滞的阶段结构种群模型的动力学

本文研究具有阶段结构的捕食者-被捕食者模型的动力学，该模型具有阶段性和依赖状态的成熟延迟。首先，提出解决方案的积极性和有界性，以描述人口的生存和有限资源的自然限制。其次，利用度数理论和劳斯·赫维兹准则研究了（边界和共存）平衡的存在性，唯一性和局部渐近稳定性。第三，获得了成熟群体最终行为的显式边界。最后，通过比较原理和两个辅助系统，