The interaction between plants and herbivores is one of the most fundamental processes in ecology. Discrete-time models are frequently used for describing the dynamics of plants and herbivores interaction with non-overlapping generations, such that a new generation replaces the old at regular time intervals. Keeping in view the interaction of the apple twig borer and the grape vine, the qualitative behaviour of a discrete-time plant–herbivore model is investigated with weak predator functional response. The topological classification of equilibria is investigated. It is proved that the boundary equilibrium undergoes transcritical bifurcation, whereas unique positive steady-state of discrete-time plant–herbivore model undergoes Neimark–Sacker bifurcation. Numerical simulation is provided to strengthen our theoretical discussion.

植物与草食动物之间的相互作用是生态学中最基本的过程之一。离散时间模型通常用于描述植物和草食动物与非重叠世代的相互作用的动力学，从而使新世代以固定的时间间隔替换了旧世代。考虑到苹果树枝bore和葡萄藤之间的相互作用，研究了捕食者功能响应较弱的离散时间植物-草食动物模型的定性行为。研究了平衡的拓扑分类。证明了边界平衡经历了跨临界分叉，而离散时间的植物-草食动物模型的唯一正稳态经历了Neimark-Sacker分叉。提供数值模拟以加强我们的理论讨论。