Impulsive perturbation and bifurcation of solutions for a model of chemostat with variable yield

doi:10.1007/s10483-009-0712-x

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	Impulsive perturbation and bifurcation of solutions for a model of chemostat with variable yield
	Zhang, Hong 1,2; Georgescu, Paul 3; Nieto, Juan J.4; Chen, Lan-sun 5
	2009-07-01
发表期刊	APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION
ISSN	0253-4827
卷号	30 期号:7 页码:933-944
摘要	In this paper, we consider a variable yield model of a single-species growth in a well-stirred tank containing fresh medium, assuming the instances of time as triggering factors in which the nutrient refilling process and the removal of microorganisms by the uptake of lethal external antibiotic are initiated. It is also assumed that the periodic nutrient refilling and the periodic antibiotic injection occur with the same periodicity, but not simultaneously. The model is then formulated in terms of autonomous differential equations subject to impulsive perturbations. It is observed that either the population of microorganisms essentially washes out, or more favorably, the system is permanent. To describe this dichotomy, some biologically significant integral conditions are introduced. Further, it is shown that in a certain critical situation, a nontrivial periodic solution emerges via a bifurcation phenomenon. Finally, the dynamics of the model is illustrated with numerical experiments and computer simulations.
关键词	chemostat impulsive differential equation permanence extinction fixed point approach bifurcation
DOI	10.1007/s10483-009-0712-x
语种	英语
WOS研究方向	Mathematics ; Mechanics
WOS类目	Mathematics, Applied ; Mechanics
WOS记录号	WOS:000268187900012
出版者	SHANGHAI UNIV
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/7581
专题	中国科学院数学与系统科学研究院
通讯作者	Zhang, Hong
作者单位	1.Jiangsu Univ, Dept Math, Zhenjiang 212013, Jiangsu Prov, Peoples R China 2.Umea Univ, Dept Math & Math Stat, SE-90187 Umea, Sweden 3.Gh Asachi Tech Univ Iasi, Dept Math, Iasi 700506, Romania 4.Univ Santiago de Compostela, Fac Matemat, Dept Anal Matemat, Santiago De Compostela 15782, Spain 5.Chinese Acad Sci, Inst Math, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Zhang, Hong,Georgescu, Paul,Nieto, Juan J.,et al. Impulsive perturbation and bifurcation of solutions for a model of chemostat with variable yield[J]. APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION,2009,30(7):933-944.
APA	Zhang, Hong,Georgescu, Paul,Nieto, Juan J.,&Chen, Lan-sun.(2009).Impulsive perturbation and bifurcation of solutions for a model of chemostat with variable yield.APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION,30(7),933-944.
MLA	Zhang, Hong,et al."Impulsive perturbation and bifurcation of solutions for a model of chemostat with variable yield".APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION 30.7(2009):933-944.