Analysis of pest population dynamic model using swallowtail catastrophe theory
害虫种群动态模型的燕尾突变分析

In this paper, we build a swallowtail catastrophe dynamic model of the pest population in a farmland ecosystem, taking into account influential factors such as crop, climate and natural enemies. From this, we derive a standard swallowtail catastrophe model and analyze the catastrophic phenomena caused by the dynamic pest population. In particular, we make a concrete analysis of the swallowtail catastrophe pattern, studying the equilibrium points and system potential functions of each control space generated by the bifurcation set of the swallowtail catastrophe, to explain the conditions and mechanisms of quantity catastrophe in the pest population. We also describe phenomena such as pest population size eruption and dynamic lag using swallowtail catastrophe theory. The results in this paper provide a theoretical basis for practical applications.