| 一类具有非线性收获率的捕食者-食饵生态经济系统的分支分析 |
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| 引用本文： | 刘唯一,;傅朝金,;陈静,;柯于胜. 一类具有非线性收获率的捕食者-食饵生态经济系统的分支分析[J]. 湖北师范学院学报(自然科学版), 2014, 0(2): 46-51 |
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| 作者姓名： | 刘唯一, 傅朝金, 陈静, 柯于胜 |
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| 作者单位： | [1]咸宁职业技术学院机电工程系,湖北咸宁437100; [2]湖北师范学院数学与统计学院,湖北黄石435002 |
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| 摘 要： | 研究了一类捕食者-食饵生态经济模型的动力学行为.该模型具有非线性收获率,这使得模型更具一般性.选取经济利润v作为分支参数,通过局部参数化方法,Hopf分支理论和形式级数方法研究了系统的Hopf分支.同时,改进的参数化计算过程更简单,能够处理更复杂的模型.最后,通过MATLAB仿真证明了我们的结果.
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| 关 键 词： | 微分代数方程 稳定性 Hopf分支 非线性收获率 改进的算法 |
Bifurcation analysis of a predator-prey biological economic system with nonlinear harvesting rate |
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| LIU Wei-yi;FU Chao-jin;CHEN Jing;KE Yu-sheng. Bifurcation analysis of a predator-prey biological economic system with nonlinear harvesting rate[J]. Journal of Hubei Normal University(Natural Science), 2014, 0(2): 46-51 |
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| Authors: | LIU Wei-yi FU Chao-jin CHEN Jing KE Yu-sheng |
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| Affiliation: | LIU Wei-yi, FU Chao-jin, CHEN Jing, KE Yu-sheng ( 1. Department of Mechanical and Electrical Engineering, Xianning Vocational Technical College, Xianning 437100, China ;2. College of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China) |
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| Abstract: | In this paper,we analyze a biological economic system with harvesting effort on prey. Different from previous researchers＇ models,this model with nonlinear harvesting rate is more general. By employing local parameterization method,Hopf bifurcation theory and the formal series method,the Hopf bifurcation of the proposed system is investigated. Here we choose economic revenue as a positive bifurcation parameter. And the improved calculation process of parameterization is much more simple and it can handle more complex models which could not be dealt with by previous algorithms due to extensive calculation. Finally,by MATLAB simulation,the validity and feasibility of obtained results are illustrated. |
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| Keywords: | differential-algebraic equations stability Hopf bifurcation nonlinear harvesting rate improved algorithm |
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