| 具有分段常数变量的捕食-被捕食模型的分支分析 |
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| 引用本文： | 陈斯养,张艳.具有分段常数变量的捕食-被捕食模型的分支分析[J].兰州大学学报(自然科学版),2012,48(3):103-112,117. |
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| 作者姓名： | 陈斯养 张艳 |
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| 作者单位： | 陕西师范大学数学与信息科学学院,西安,710062 |
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| 摘 要： | 讨论了具有分段常数变量的捕食与被捕食模型的稳定性与分支分析.利用Jury判据得到模型正平衡态局部渐近稳定、不稳定的充分条件;应用中心流形定理和分支理论给出模型存在分支的条件;通过实例验证定理条件与结论的可实现性并说明了在一定条件下模型动力学行为的复杂性.
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| 关 键 词： | 分段常数变量 Flip分支 Hopf分支 Neimark-Sacker分支 稳定性 |
Stability and bifurcation analysis of a predator-prey model with piecewise constant arguments |
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| CHEN Si-yang
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ZHANG Yan.Stability and bifurcation analysis of a predator-prey model with piecewise constant arguments[J].Journal of Lanzhou University(Natural Science),2012,48(3):103-112,117. |
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| Authors: | CHEN Si-yang ZHANG Yan |
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| Institution: | College of Mathematics and Information Science,Shaanxi Normal University,Xi’an 710062,China |
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| Abstract: | The stability of equilibrium point of a predator-prey model with piecewise constant arguments and bifurcation analysis was investigated.Sufficient conditions for the local asymptotically stability and non-stability of this model were derived by using the Jury criterion.Furthermore,conditions for the existence of bifurcation were discussed by applying the center manifold theorem.Finally,some numerical examples supporting our theoretical predictions and the complexity dynamic behaviors under certain conditions were also given. |
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| Keywords: | piecewise constant argument Flip branch Hopf branch Neimark-Sacker branch stability |
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