| 摘要: |
| 本文研究了一类用更为合理的无选择性捕获函数来代替普通的单位捕捞鱼获量函数的微分代数经济系统. 利用范式定理和中心流形定理, 获得了生物经济系统内平衡点局部稳定和Hopf分支的稳定性,改进和推广了已有的结果. 最后, 用数值模拟来证明分析结果的有效性. |
| 关键词: 局部稳定性 时滞 Hopf分支 比例相关 |
| DOI： |
| 分类号:O193 |
| 基金项目:Supported by National Natural Science Foundation of China (10671182). |
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| HOPF BIFURCATION IN A DELAYED DIFFERENTIAL-ALGEBRAIC ECONOMIC SYSTEM WITH A RATE-DEPENDENT HARVESTING |
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WANG Gan, CHEN Bo-shan, LI Meng, LI Zhen-wei
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College of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China
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| Abstract: |
| In this paper, we study a differential-algebraic biological economic system with time delay and non-selective harvesting which is a reasonable catch-rate function instead of usual catch-per-unit-effort hypothesis. By using the normal form approach and the center manifold the-ory, we obtain the stability and the Hopf bifurcation of the differential-algebraic biological economic system, which generalize and improve some known results. Finally, numberical simulations are per-formed to illustrate the analytical results. |
| Key words: local stability time delay Hopf bifurcation ratio-dependent |
