Qualitative analysis of impulsive state feedback control to an algae-fish system with bistable property

doi:10.1016/j.amc.2015.09.046

CSpace

	Qualitative analysis of impulsive state feedback control to an algae-fish system with bistable property
	Guo, Hongjian 1; Chen, Lansun 2; Song, Xinyu 1
	2015-11-15
发表期刊	APPLIED MATHEMATICS AND COMPUTATION
ISSN	0096-3003
卷号	271 页码:905-922
摘要	A kind of consumer-resource system is proposed to describe the bidirectional interactions of the algae and the fish in an eutrophic water body. The dynamical properties of the proposed continuous system are given. For the bistable case, an impulsive semidynamical system with state feedback control, which depends on the biomass of the algae, is formulated and investigated to consider the feasibility of state feedback control for the aim of maintaining two species coexisting. The impulsive semidynamical system has three cases corresponding to three kinds of control measures: releasing fish, spraying algaecide, integrated control combining releasing fish and spraying algaecide. The existences of order-1 periodic solutions of three models are discussed by using successor function, respectively. The conditions under which the order-1 periodic solution is stable are given by using the Poincare map and the analogue of Poincare criterion. Mathematical results show that, for every one of three control strategies, there exists a range of control parameter in which the corresponding control is feasible. Finally, those mathematical results are verified by numerical simulations and the practical meanings are given. (C) 2015 Elsevier Inc. All rights reserved.
关键词	Consumer-resource system Impulsive semidynamical system Impulsive state feedback control Bistability Order-k(k >= 1) periodic solution Orbital stability
DOI	10.1016/j.amc.2015.09.046
语种	英语
资助项目	National Natural Science Foundation of China[11371306] ; National Natural Science Foundation of China[11171284] ; Program for Science and Technology Innovation Talents in Universities of Henan Province[14HASTIT046]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000367819300012
出版者	ELSEVIER SCIENCE INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/21677
专题	中国科学院数学与系统科学研究院
通讯作者	Guo, Hongjian
作者单位	1.Xinyang Normal Univ, Coll Math & Informat Sci, Xinyang 464000, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Guo, Hongjian,Chen, Lansun,Song, Xinyu. Qualitative analysis of impulsive state feedback control to an algae-fish system with bistable property[J]. APPLIED MATHEMATICS AND COMPUTATION,2015,271:905-922.
APA	Guo, Hongjian,Chen, Lansun,&Song, Xinyu.(2015).Qualitative analysis of impulsive state feedback control to an algae-fish system with bistable property.APPLIED MATHEMATICS AND COMPUTATION,271,905-922.
MLA	Guo, Hongjian,et al."Qualitative analysis of impulsive state feedback control to an algae-fish system with bistable property".APPLIED MATHEMATICS AND COMPUTATION 271(2015):905-922.