Li Xiong, Wang Hao, Kuang Yang
Laboratory of Mathematics and Complex Systems, School of Mathematical Sciences, Beijing Normal University, Ministry of Education, Beijing, People's Republic of China.
J Math Biol. 2011 Nov;63(5):901-32. doi: 10.1007/s00285-010-0392-2. Epub 2011 Jan 14.
Cells, the basic units of organisms, consist of multiple essential elements such as carbon, nitrogen, and phosphorus. The scarcity of any of these elements can strongly restrict cellular and organismal growth. During recent years, ecological models incorporating multiple elements have been rapidly developed in many studies, which form a new research field of mathematical and theoretical biology. Among these models, the one proposed by Loladze et al. (Bull Math Biol 62:1137-1162, 2000) is prominent and has been highly cited. However, the global analysis of this nonsmooth model has never been done. The aim of this paper is to provide the complete global analysis for the model with Holling type I functional response and perform a bifurcation analysis for the model with Holling type II functional response.
细胞作为生物体的基本单位，由碳、氮、磷等多种必需元素组成。这些元素中任何一种的稀缺都会强烈限制细胞和生物体的生长。近年来，许多研究中迅速发展出了包含多种元素的生态模型，这形成了数学和理论生物学的一个新研究领域。在这些模型中，洛拉泽等人（《数学生物学通报》62:1137 - 1162，2000年）提出的模型很突出且被大量引用。然而，这个非光滑模型的全局分析从未进行过。本文的目的是对具有Holling I型功能反应的模型进行完整的全局分析，并对具有Holling II型功能反应的模型进行分岔分析。
