This paper studies the periodic trajectories of a novel age-structured prey–predator system with Michaelis–Menten functional response including delays and asymmetric diffusion. To begin with, the system is turned into an abstract non-densely defined Cauchy problem, and a time-lag effect in their interaction is investigated. Next, we acquire that this system appears a periodic orbit near the positive steady state by employing the method of integrated semigroup and the Hopf bifurcation theory for semilinear equations with non-dense domain, which is also the main result of this article. Finally, in order to illustrate our theoretical analysis more vividly, we make some numerical simulations and give some discussions.

本文研究了具有 Michaelis-Menten 功能响应（包括延迟和不对称扩散）的新型年龄结构的猎物 - 捕食者系统的周期性轨迹。首先，将系统转化为抽象的非密集定义的柯西问题，并研究它们相互作用中的时滞效应。接下来，我们利用积分半群的方法和非稠域半线性方程组的Hopf分岔理论得到了该系统在正稳态附近出现了一个周期轨道，这也是本文的主要成果。最后，为了更形象地说明我们的理论分析，我们做了一些数值模拟并给出了一些讨论。