一类榕树–榕小蜂互惠共生模型的动力学分析

Dynamical Analysis of a Fig-Fig Wasp Mutualism Model

摘要: 榕树与榕小蜂是自然界中典型的共生系统，榕树为榕小蜂产卵提供场所，榕小蜂为榕树传粉，并且榕树会对不传粉只产卵的榕小蜂实施宿主惩罚，以限制其过度繁殖。基于榕树和榕小蜂典型的互惠共生关系，我们建立了包含榕小蜂传粉、产卵以及宿主惩罚的榕–蜂互惠共生模型，并利用微分方程定性理论，研究了该模型的种群动力学及其分岔行为，证明了系统存在双稳态现象及其产生机制。

Abstract: Fig-fig wasp is a classic mutualistic system in nature. Fig provides a site for the fig wasp to lay eggs, while the fig wasp pollinates the fig, enabling seed production. Moreover, the fig imposes host sanctions on wasps that lay eggs without pollinating in order to limit their excessive reproduction. Based on this mechanism, we consider a model of fig-fig wasp mutualism, incorporating the pollination rate, the oviposition rate of the wasps and the threshold for tolerating oviposition. By the qualitative theory of ordinary differential equations, we study the population dynamics of the model and its bifurcation. We show that the system exhibits bistability.