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Modeling and analysis in a prey-predator system with commercial harvesting and double time delays
Liu C(刘超); Lu, Na; Zhang QL(张庆灵); Li JN(李金娜); Liu, Peiyong
作者部门工业控制网络与系统研究室
关键词Maturation Delay Gestation Delay Economic Interest Singularity Induced Bifurcation State Feedback Control Hopf Bifurcation
发表期刊Applied Mathematics and Computation
ISSN0096-3003
2016
卷号281页码:77-101
收录类别SCI ; EI
EI收录号20160701953642
WOS记录号WOS:000371338700006
产权排序4
资助机构National Natural Science Foundation of China, grant no. 61104003 and grant no. 61273008. Research Program for Liaoning Excellent Talents in University, grant no. LJQ2014027. Hebei Province Natural Science Foundation, grant no. F2015501047. Hong Kong Admission Scheme for Mainland Talents and Professionals, Hong Kong Special Administrative Region.
摘要A differential-algebraic prey-predator system with commercial harvesting on predator is proposed, where maturation delay for prey and gestation delay for predator are considered. Since commercial harvesting is dynamically influenced by variation of economic interest, we will investigate combined dynamic effects of double time delays and economic interest on population dynamics. Positivity of solutions and uniform persistence of system are studied. In the absence of time delay, by taking economic interest as bifurcation parameter, existence of singularity induced bifurcation is investigated based on differential-algebraic system theory. State feedback controllers are designed to eliminate singularity induced bifurcation and stabilize the proposed system around corresponding interior equilibrium. In the presence of double time delays, by analyzing associated characteristic transcendental equation, it is found that interior equilibrium loses local stability when double time delays cross corresponding critical values. According to Hopf bifurcation theorem for functional differential equation, existence of Hopf bifurcation is investigated as local stability switches. Based on normal form theory and center manifold theorem, directions of Hopf bifurcation and stability of the bifurcating periodic solutions are studied. Numerical simulations are carried out to show consistency with theoretical analysis.
语种英语
WOS标题词Science & Technology ; Physical Sciences
WOS类目Mathematics, Applied
关键词[WOS]BIFURCATION-ANALYSIS ; FUNCTIONAL-RESPONSE ; HOPF-BIFURCATION ; STABILITY ; RESOURCE ; BEHAVIOR ; FISHERY
WOS研究方向Mathematics
引用统计
文献类型期刊论文
条目标识符http://ir.sia.cn/handle/173321/17642
专题工业控制网络与系统研究室
通讯作者Liu C(刘超)
作者单位1.Institute of Systems Science, Northeastern University, Shenyang, China
2.Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong
3.State Key Laboratory of Integrated Automation of Process Industry, Shenyang, China
4.Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang, China
5.College of Life and Health Science, Northeastern University, Shenyang, China
推荐引用方式
GB/T 7714
Liu C,Lu, Na,Zhang QL,et al. Modeling and analysis in a prey-predator system with commercial harvesting and double time delays[J]. Applied Mathematics and Computation,2016,281:77-101.
APA Liu C,Lu, Na,Zhang QL,Li JN,&Liu, Peiyong.(2016).Modeling and analysis in a prey-predator system with commercial harvesting and double time delays.Applied Mathematics and Computation,281,77-101.
MLA Liu C,et al."Modeling and analysis in a prey-predator system with commercial harvesting and double time delays".Applied Mathematics and Computation 281(2016):77-101.
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