| 带有非线性收获和妊娠时滞的微分代数捕食者-食饵系统的稳定性及Hopf分支 |
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| 引用本文： | 李蒙,陈伯山,李必文.带有非线性收获和妊娠时滞的微分代数捕食者-食饵系统的稳定性及Hopf分支[J].数学杂志,2016,36(5):993-1004. |
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| 作者姓名： | 李蒙 陈伯山 李必文 |
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| 作者单位： | 湖北师范大学数学统计学院, 湖北 黄石 435002,湖北师范大学数学统计学院, 湖北 黄石 435002,湖北师范大学数学统计学院, 湖北 黄石 435002 |
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| 基金项目： | Supported by the Project of Higher School Outstanding Youth Scientific and Technological Innovation Team of Hubei Province (T201412). |
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| 摘 要： | 本文研究了一类同时带有非线性食饵收获和捕食者妊娠时滞的微分代数捕食者-食饵系统的稳定性及Hopf分支问题.利用了分支理论和稳定性理论,以捕食者妊娠时滞作为系统的分支参数,获得了所提出的新系统在正平衡点处系统稳定性的相关判据条件和Hopf分支的产生条件.推广了一般带有线性收获和时滞的微分代数捕食者-食饵系统的结论.
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| 关 键 词： | 生物经济学 微分代数系统 非线性收获 妊娠时滞 Hopf分支 稳定性 |
| 收稿时间： | 2014/4/14 0:00:00 |
| 修稿时间： | 2014/6/23 0:00:00 |
STABILITY AND HOPF BIFURCATION FOR A DIFFERENTIAL ALGEBRAIC PREDATOR-PREY SYSTEM WITH NONLINEAR HARVESTING AND GESTATIONAL TIME DELAY |
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| LI Meng,CHEN Bo-shan and LI Bi-wen.STABILITY AND HOPF BIFURCATION FOR A DIFFERENTIAL ALGEBRAIC PREDATOR-PREY SYSTEM WITH NONLINEAR HARVESTING AND GESTATIONAL TIME DELAY[J].Journal of Mathematics,2016,36(5):993-1004. |
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| Authors: | LI Meng CHEN Bo-shan and LI Bi-wen |
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| Institution: | School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China,School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China and School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China |
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| Abstract: | In this paper, we investigate the stability and Hopf bifurcation for a new differential algebraic predator-prey system which combined with nonlinear harvesting in prey and gestational time delay of predator. Using bifurcation theorem and stability theorem, through considering gestational time delay of predator as bifurcation parameter, we obtain the interrelated stability criterion and the related conditions of producing Hopf bifurcation at the positive equilibrium point of the proposed system, which popularize the conclusions of the general differential algebraic predator-prey system which combined with linear harvesting and time delay. |
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| Keywords: | biological economic differential algebraic system nonlinear harvesting gestational time delay Hopf bifurcation stability |
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