In this paper, an ecological model described by a couple of state-dependent impulsive equations is studied analytically and numerically. The theoretical analysis suggests that there exists a semitrivial periodic solution under some conditions and it is globally orbitally asymptotically stable. Furthermore, using the successor function, we study the existence, uniqueness, and stability of order-1 periodic solution, and the boundedness of solution is also presented. The relationship between order- successor function and order- periodic solution is discussed as well, thereby giving the existence condition of an order-3 periodic solution. In addition, a series of numerical simulations are carried out, which not only support the theoretical results but also show the complex dynamics in the model further, for example, the coexistence of multiple periodic solutions, chaos, and period-doubling bifurcation.

中文翻译：

---

具有状态依赖型脉冲控制策略的捕食者模型的动态复杂性

本文分析和数值研究了由两个状态相关的脉冲方程描述的生态模型。理论分析表明，在某些条件下存在半平凡的周期解，并且它在全局轨道上是渐近稳定的。此外，利用后继函数，研究了1阶周期解的存在性，唯一性和稳定性，并给出了该解的有界性。订单后继功能与订单之间的关系还讨论了周期解，从而给出了三阶周期解的存在条件。此外，进行了一系列数值模拟，不仅支持理论结果，而且还进一步显示了模型中的复杂动力学，例如，多个周期解，混沌和倍增分岔并存。