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具比率依赖型HollingⅡ功能反应函数的两种群系统的最优税收策略 被引量：2

Optimal Taxation Policv to a Two-Species System with Ratio-Dependent and HollingⅡFunctional Response
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摘要 研究了具比率依赖型功能性反应函数的两种群系统,利用微分方程定性理论得到了系统正平衡点的存在性、局部渐近稳定性及全局渐近稳定性的条件,并且由Pontryagin最大值原理得到了最优税收策略. In this paper,a two-species system with ratio-dependent and functional response is studied.The existence of positive equilibrium of the system is discussed,and under certain conditions,the positive equilibrium are local and global stable.An optimal taxation policy is obtained by Pontryagin＇s maximum principle.
作者 张九娥 雒志学 王利红 王振禄
机构地区 兰州交通大学数学系 兰州城市学院
出处 《数学研究》 CSCD 2010年第4期411-416,共6页 Journal of Mathematical Study
基金 国家自然科学基金资助项目(11061017) 甘肃省自然科学基金(1010RJZA075)
关键词 食饵-捕食者 平衡点 局部渐近稳定 全局渐近稳定 最优税收 Ratio-dependent Prey-predator Local asymptotic stable Global asymptotic stable Optimal taxation
分类号 O175 [理学—基础数学]
  • 相关文献

参考文献7

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二级参考文献10

  • 1Ganguly S, Chaudhur K S. Regulation of a single-species fishery by taxation[J].Ecological Modeling, 1995,82:51-60.
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共引文献14

同被引文献15

  • 1Chen Feng - de. On a Leslie - Gower predator - prey model incorporating a prey refuge [ J ]. Nonlinear Analysis : Real World Applications, 2009 (10) : 2 905 - 2 908.
  • 2Kar T K. Conservation of a fishery through optimal taxation: a dynamic reaction model [ J ]. Communications in Nonlinear Science and Numerical Simulation, 2005(10) : 121 - 131.
  • 3陈兰荪,宋新宇,陆征一.数学生态学模型与研究方法[M].成都:四川科学技术出版社,2006.
  • 4Clark C W. Mathematical bioeconomics: the optimal management of renewable resources[ M]. New York: John Whiley, 1976.
  • 5CLARK C W. Mathematical Bioeconomics: The Optimal Management of Renewable Resources [M]. 2nd ed. NewY ork: W iley,1990.
  • 6DAI G R, TANG M X. Coexistence Region and Global Dynamics of a Harvested Predator-prey System [J]. SIAM J ApplM ath, 1998, 58(1) : 193-210.
  • 7ZHAO Z, ZHANG X Q, CHEN L S. The Effect of Pulsed Harvesting Policy on the Inshore-Offshore Fishery Modelwith the Impulsive Diffusion [J]. Nonlinear Dynamics,2011,63(4) : 537 -545.
  • 8KAR T K , CHAUDHURI K S. Regulation of a Prey-predator Fishery by Taxation: A Dynamic Reaction Model [J]. JBiol Syst,2003, 11(2): 173 - 187.
  • 9DUBEY B, SINHA P, CHANDRA P. A Model for an Inshore-Offshore Fishery [J]. J Biol Syst, 2003, 11 ( 1 ) :2 7 -4 1 .
  • 10KAR T K , PAHARI U K , CHAUDHURI K S. Management of a Single Species Fishery with Stage-Structure [J]. InternationalJournal of Mathematical Education in Science and Technology, 2004,35(3) : 403 - 414.

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数学研究
2010年 第4期

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