| 一类具有时滞和Gompertz增长率的捕食系统的稳定性与Hopf分支 |
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| 引用本文： | 王海彬,徐瑞,耿立杰.一类具有时滞和Gompertz增长率的捕食系统的稳定性与Hopf分支[J].军械工程学院学报,2013(2):70-75. |
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| 作者姓名： | 王海彬 徐瑞 耿立杰 |
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| 作者单位： | 军械工程学院基础部,河北石家庄050003 |
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| 基金项目： | 国家自然科学基金资助项目（11071254） |
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| 摘 要： | 研究一类具有时滞和Gompertz增长率的捕食系统，通过分析系统的特征方程，得到正平衡点的局部稳定性和系统出现Hopf分支的条件，并利用中心流形定理和规范型理论，得到确定Hopf分支方向和分支周期解稳定性的计算公式．
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| 关 键 词： | 时滞 Hopf分支 稳定性 功能反应函数 周期解 |
Stability and Bifurcation Analysis of a Predator Prey System with Time Delay and Gompertz Growth Rate |
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| WANG Hai-bin,XU Rui,GENG Li-jie.Stability and Bifurcation Analysis of a Predator Prey System with Time Delay and Gompertz Growth Rate[J].Journal of Ordnance Engineering College,2013(2):70-75. |
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| Authors: | WANG Hai-bin XU Rui GENG Li-jie |
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| Institution: | (Basic Courses Department, Ordnance Engineering College, Shijiazhuang 050003, China) |
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| Abstract: | In this paper, a predator prey system with time delay and Gompertz growth rate is inves- tigated. By analyzing the associated characteristic equation of the system,the local stability of the positive equilibrium and the existence of Hopf bifurcations are established. Based on the normal form theory and center manifold reduction, explicit formulae are derived which determine the sta- bility and direction of the bifurcating periodic solutions. |
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| Keywords: | time delay Hopf bifurcation stability functional response periodic solution |
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