| 一类具有时滞和HollingⅢ类功能性反应的捕食系统的稳定性与Hopf分支 |
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| 引用本文： | 陈辉,徐瑞.一类具有时滞和HollingⅢ类功能性反应的捕食系统的稳定性与Hopf分支[J].吉林林学院学报,2014(2):141-148. |
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| 作者姓名： | 陈辉 徐瑞 |
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| 作者单位： | 军械工程学院应用数学研究所,河北石家庄050003 |
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| 基金项目： | 国家自然科学基金项目（11071254）. |
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| 摘 要： | 研究一类具有时滞和Hollingm类功能性反应的捕食系统，通过分析系统的特征方程，研究了正平衡点的局部稳定性，得到了系统出现Hopf分支的条件，利用中心流形定理和规范型理论，得到了确定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 功能性反应 Hopf分支 稳定性 |
Stability and Hopf Bifurcation of a Class Predator System with Time Delay and Holling Type III Functional Response |
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| Authors: | CHEN Hui XU Rui |
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| Institution: | ( Institute of Applied Mathematics, Ordnance Engineering College, Shijiazhuang 050003, China ) |
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| Abstract: | A predator-prey system with time delay and Holling type III functional response is investigated. By analyzing the associated characteristic equations 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 to determine the stability and direction of Hopf bifurcation periodic solutions. |
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| Keywords: | time delay functional response Hopf bifurcation stability |
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