arXiv 2003.079412020-03math.DSq-bio.PE

植物挥发性物质与三营养相互作用的动态

Dynamics of tritrophic interaction with volatile compounds in plants

Arturo J. Nic May, Eric J. Avila Vales

备注：: 18 pages, 10 figures, minor corrections, we modify the proof of theorem 3

摘要：

在本文中，我们将考虑一个数学模型，描述，植物，食草动物和它们的天敌之间的三营养相互作用，其中挥发性有机化合物（VOCs）释放的植物起着重要的作用。我们证明了系统解的正性和有界性，正平衡点的存在性及其局部稳定性，利用Li和Muldowney的几何方法分析了正平衡点的全局稳定性.我们注意参数，以讨论不同类型的分歧。最后，我们提出了一些数值模拟来证明我们的分析结果。

英文摘要：

In this paper we will consider a mathematical model that describes, the tritrophic interaction between plants, herbivores and their natural enemies, where volatiles organic compounds (VOCs) released by plants play an important role. We show positivity and boundedness of the system solutions, existence of positive equilibrium and its local stability, we analyse global stability of positive equilibrium via the geometrical approach of Li and Muldowney. We pay attention to parameters in order to discuss different types of bifurcations. Finally, we present some numerical simulations to justify our analytical results.

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