| 具有时滞的稀疏效应捕食-被捕食模型的分支分析 |
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| 引用本文： | 徐昌进,张千宏.具有时滞的稀疏效应捕食-被捕食模型的分支分析[J].河北师范大学学报(自然科学版),2012,36(1):1-7,20. |
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| 作者姓名： | 徐昌进 张千宏 |
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| 作者单位： | 贵州财经学院贵州省经济系统仿真重点实验室,贵州贵阳,550004 |
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| 基金项目： | 国家自然科学基金，湖南省科技计划资助项目，湖南省教育厅资助科研项目，贵州财经学院博士科研基金 |
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| 摘 要： | 研究了一类有时滞的稀疏效应捕食-被捕食模型.选择时滞τ为分支参数,得到了当时滞τ通过一系列的临界值时,Hopf分支产生,即当时滞τ通过某些临界值时,从平衡点处产生一簇周期解.利用规范型及中心流形理论,得到了确定Hopf分支的稳定性及方向的具体算式.最后,用数值模拟验证了分析结果的正确性.
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| 关 键 词： | 捕食-被捕食 Hopf分支 稳定性 稀疏效应 |
Bifurcation Analysis for a Delayed Predator-prey Model with Undercrowding Effect |
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| XU Changiin
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ZHANG Qianhong.Bifurcation Analysis for a Delayed Predator-prey Model with Undercrowding Effect[J].Journal of Hebei Normal University,2012,36(1):1-7,20. |
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| Authors: | XU Changiin ZHANG Qianhong |
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| Institution: | (Guizhou Key Laboratory of Economics System Simulation,Guizhou College of Finance and Economics,Guizhou Guiyang 550004,China) |
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| Abstract: | A delayed predator-prey model with undercrowding effect is investigated.By choosing the delay τ as a bifurcation parameter,that Hopf bifurcation can occur when τ passes a sequence of critical values is shown.This means that a family of periodic solutions bifurcate from the equilibrium when the bifurcation parameter exceeds a critical value some explicit for mulae for determining the stability and the direction of the Hopf bifurcation are obtained by using the normal form theory and center mamifold theory.Some numerical simulations are given to justify the theoretical analysis results. |
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| Keywords: | predator-prey Hopf bifurcation stability undercrowding effect |
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