Global stability analysis and optimal taxation strategy for a prey-predatorsystem with prey population refuge

LIU Chao; ZHANG Yi; ZHANG Qingling; LI Yuanke

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Global stability analysis and optimal taxation strategy for a prey-predatorsystem with prey population refuge

LIU Chao 1,ZHANG Yi 2,ZHANG Qingling 3 *,LI Yuanke 4

1.State Key Laboratory of Integrated Automation of Process Industry, Northeastern University, Shenyang, 110819

2.State Key Laboratory of Integrated Automation of Process Industry, Northeastern University, Shenyang 110819

3.State Key Laboratory of Integrated Automation of Process Industry, Northeastern University, ShenYang 110819

4.School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066004

*Correspondence author

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Funding: Research Foundation for Doctor-al Program of Higher Education of Education Ministry（No.20110042120016）, National Natural Science Foundation of China（No.61104003,61273008）, Fundamental Research Funds for the Central Universities of Education Ministry（No.N120423009）, Research Foundation for Science and Technology Pillar Program of Northeastern University at Qinhuangdao（No.XNK201301）, Hebei Province Natural Science Foundation（No.F2011501023）

Opened online:16 May 2013

Accepted by: none

Citation: LIU Chao,ZHANG Yi,ZHANG Qingling .Global stability analysis and optimal taxation strategy for a prey-predatorsystem with prey population refuge[OL]. [16 May 2013] http://en.paper.edu.cn/en_releasepaper/content/4542526

In this paper, a prey predator system with prey refuge is proposed, where selective harvest effort on predator population is considered and taxation is utilized as a control instrument to protect the predator population from overexploitation. Conditions which influence boundedness of positive solutions of model system are studied. By using differential dynamical system theory, local stability analysis around all equilibria of system are discussed due to variation of prey refuge level and taxation. Furthermore, global stability of system around the positive equilibrium is investigated based on Bendixson criterion. By using Pontryagin's maximum principle, an optimal taxation policy is derived to ensure the sustainable development of related population resource and prosperous commercial harvesting.

Keywords:Operations research and control theory; prey predator; harvest effort; prey refuge; optimaltaxation policy; global stability analysis

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