Multiple limit cycles in an immune system
type: Item
instance of: scholarly article
title: Multiple limit cycles in an immune system
zbMATH Open document ID: 1156.34037
author: Le-Min Zhu
author: Minaya Villasana
author: Xun-Cheng Huang
published in: Acta Mathematicae Applicatae Sinica. English Series
publication date: 2008-09-08T00:00:00Z
review text: Predator-prey model in immunology in which the replication of antigens requires some kind of nutrient is important in understanding the dynamics of immune response systems. Such systems may exhibit nonlinear oscillatory phenomena which correspond to the cycles in mathematical models. The authors analyze an immune response system first proposed by \textit{X. C. Huang} [Int. J. Syst. Sci. 22, No.~3, 579--585 (1991; Zbl 0751.92009)], and show that it has at least three limit cycles, which is in contrast with the uniqueness of limit cycles of the latter. The conditions for multiple limit cycles are useful in analyzing the nonlinear oscillation in immune response. The mathematics is quite robust, but the manuscript is not carefully edited.
Mathematics Subject Classification ID: 34C60
Mathematics Subject Classification ID: 92C60
Mathematics Subject Classification ID: 34C05
zbMATH DE Number: 5322522
zbMATH Keywords: immune response
zbMATH Keywords: multiple limit cycles
zbMATH Keywords: oscillation
reviewed by: J. Michel Tchuenche
MaRDI profile type: Publication
full work available at URL: s10255-005-5040-z
OpenAlex ID: W2395732441
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DOI: 10.1007/S10255-005-5040-Z
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description: scientific article; zbMATH DE number 5322522