Journal of Mathematical Biology

, Volume 63, Issue 5, pp 901–932 | Cite as

Global analysis of a stoichiometric producer–grazer model with Holling type functional responses

  • Xiong Li
  • Hao WangEmail author
  • Yang Kuang


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.


Stoichiometry Producer Grazer Nutrient Light Holling type functional response Global stability Limit cycle Bifurcation 

Mathematics Subject Classification (2000)

34-XX 92-XX 37-XX 58-XX 


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Laboratory of Mathematics and Complex SystemsSchool of Mathematical Sciences, Beijing Normal University, Ministry of EducationBeijingPeople’s Republic of China
  2. 2.Department of Mathematical and Statistical SciencesUniversity of AlbertaEdmontonCanada
  3. 3.School of Mathematical and Statistical SciencesArizona State UniversityTempeUSA

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