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 引用本文: 何泽荣, 王绵森, 王峰. 一类可再生资源系统的最优动态平衡收获[J]. 应用数学和力学, 2004, 25(4): 433-440.
HE Ze-rong, WANG Mian-se, WANG Feng. Optimal Dynamical Balance Harvesting for a Class of Renewable Resources System[J]. Applied Mathematics and Mechanics, 2004, 25(4): 433-440.
 Citation: HE Ze-rong, WANG Mian-se, WANG Feng. Optimal Dynamical Balance Harvesting for a Class of Renewable Resources System[J]. Applied Mathematics and Mechanics, 2004, 25(4): 433-440.

## 一类可再生资源系统的最优动态平衡收获

###### 作者简介:何泽荣(1963- ),男,重庆万州人,副教授,博士(Tel:+86-571-88079706;Fax:+86-571-86919031;E-mail:hezerong@263.net).
• 中图分类号: O175.1

## Optimal Dynamical Balance Harvesting for a Class of Renewable Resources System

• 摘要: 研究一类可再生资源系统的最优利用问题．首先，引进一个新的效用函数， 它依赖于收获努力度和资源量，由此导出最优控制问题．其次证明该控制问题最优解的存在性．然后，利用无穷区间上控制问题的最大值原理，得到一个非线性的四维最优系统．通过对上述系统正平衡解的详细分析，借助 Hopf 分支定理证明了极限环的存在性．之后考虑中心流形上的简化系统， 分析极限环的稳定性．最后，解释所得结果的生物经济学意义．
•  [1] Clark C W.Mathematical Bioeconomics: the Optimal Management of Renewable Resources[M].2ed.New York: John Wiley & Sons,Inc, 1990, 39—340. [2] Mesterton-Gibbons M. On the optimal policy for combined harvesting of independent species[J].Natural Resources Modelling,1987,2(1):109—134. [3] Mesterton-Gibbons M. On the optimal policy for combined harvesting of predator and prey[J].Natural Resources Modelling,1988,3(1):63—89. [4] Mesterton-Gibbons M. A technique for finding optimal two-species harvesting policies[J].Ecological Modelling,1996,92(2): 235—244. [5] Pradham T, Chaudhuri K S. A dynamical reaction model of a two-species fishery with taxation as a control instrument: a capital theoretic analysis[J].Ecological Modelling，1999,121(3):1—16. [6] Fan M, Wang K. Optimal harvesting policy for single population with periodic coefficients[J]. Math Biosci,1998,152(1): 165—177. [7] Feichtinger G, Novok A,Wirl F. Limit cycles in intertemporal adjustment models[J].J Economic Dynamics and Control, 1994,18(2):353—380. [8] Dockner E. Local stability analysis in optimal control problems with two state variables[A]. In: Feichtinger G Ed.Optimal Control Theory and Economic Analysis[C]. Amsterdam:North-Holland, 1987, 30—45. [9] Liski M, Kort P M, Novak A. Increasing returns and cycles in fishing[J].Resources and Energy Economics,2001,23(4):241—258. [10] Seierstad K, Sydsaeter A. Optimal Control Theory With Economic Applications[M].Amsterdam: North-Holland, 1987,8—25. [11] Carlson D, Haurie A B,Leizarowits A.Infinite Horizon Optimal Control[M]. Berlin: Springer-Verlag, 1991, 24—27. [12] Guckenheimer J, Holmes P.Nonlinear Oscillations,Dynamical Systems, and Bifurcations of Vector Fields[M]. Berlin:Springer-Verlag, 1983, 117—125.
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##### 出版历程
• 收稿日期:  2002-05-03
• 修回日期:  2003-09-09
• 刊出日期:  2004-04-15

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