| 一类具有稀疏效应Volterra模型的稳定性 |
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| 引用本文： | 刘双,朱长荣,李坤琼.一类具有稀疏效应Volterra模型的稳定性[J].西南师范大学学报(自然科学版),2011,36(6). |
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| 作者姓名： | 刘双 朱长荣 李坤琼 |
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| 作者单位： | 重庆大学数学与统计学院;重庆工业职业技术学院流通管理系基础部基础教研室; |
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| 基金项目： | 中央高校基金资助项目(CDJXS11100027) |
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| 摘 要： | 研究了一类具有稀疏效应的Volterra模型的动力性态.分析发现,系统最多有3个平衡点.用规范形研究表明,在不同的参数范围下,这3个平衡点可以是鞍点、稳定结点、不稳定的结点、鞍结点和弱中心.利用第一Lyapunov系数方法,证明了系统在弱中心附近发生超临界Hopf分支,并在弱中心附近分支出唯一的极限环;利用Poincare-Bendison定理,证明了系统在不稳定平衡点时,总存在极限环.
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| 关 键 词： | 稀疏效应 平衡点 弱中心 Hopf分支 |
The Stability of a Volterra Model with Sparse Effect |
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| LIU Shuang,ZHU Chang-rong,LI Kun-qiong .College of Mathematics , Statistics,Chongqing University,Chongqing ,China,.Transportable Management.The Stability of a Volterra Model with Sparse Effect[J].Journal of Southwest China Normal University(Natural Science),2011,36(6). |
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| Authors: | LIU Shuang ZHU Chang-rong LI Kun-qiong College of Mathematics Statistics Chongqing University Chongqing China Transportable Management |
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| Institution: | LIU Shuang1,ZHU Chang-rong1,LI Kun-qiong2 1.College of Mathematics and Statistics,Chongqing University,Chongqing 401331,China,2.Transportable Management Department/Basic-Course Teaching Department,Chongqing Industry Polytechnic College,Chongqing 400050 |
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| Abstract: | The dynamical behaviors a Volterra model with sparse effect are discussed.The system is shown to have three equilibrium points at most.By the normal form theory,these equilibrium points may be saddle point,stable node,unstable node,saddle-node or weak center,depending on the ranges of parameters.By using the first Lyapunov number,it is proved that the system undergoes a supercritical Hopf bifurcation and hence a unique stable limit cycle occurs.By using the Poincare-Bendison theorem,it is proved that the sy... |
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| Keywords: | sparse effect equilibrium point weak center Hopf bifurcation |
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