| 一类非线性系统的周期扰动Hopf分支 |
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| 引用本文： | 殷红燕.一类非线性系统的周期扰动Hopf分支[J].纯粹数学与应用数学,2014(3):240-244. |
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| 作者姓名： | 殷红燕 |
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| 作者单位： | 中南民族大学数学与统计学学院,湖北武汉430074 |
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| 基金项目： | 中央高校基本科研业务费专项资金（CZQ13016） |
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| 摘 要： | 研究了小周期扰动对一类存在Hopf分支的非线性系统的影响.特别是应用平均法讨论了扰动频率与Hopf分支固有频率在共振及二阶次调和共振的情形周期解分支的存在性.表明了在某些参数区域内,系统存在调和解分支和次调和解分支,并进一步讨论了二阶次调和分支周期解的稳定性.
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| 关 键 词： | Hopf分支 平均法 调和解分支 次调和解分支 稳定性 |
Periodically perturbed Hopf bifurcation of a kind of nonlinear systems |
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| Yin Hongyan.Periodically perturbed Hopf bifurcation of a kind of nonlinear systems[J].Pure and Applied Mathematics,2014(3):240-244. |
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| Authors: | Yin Hongyan |
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| Institution: | Yin Hongyan (College of Mathematics and Statistics, South-Central University for Nationalities Wuhan 430074, China) |
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| Abstract: | The influence of small periodic perturbations on a kind of nonlinear systems exhibiting Hopf bifurcation is studied. In particular, we discuss the existence of bifurcating periodic solutions in the case that the excitation frequency and the critical natural frequency of Hopf bifurcation is resonance and subharmonic resonance. In this work, the ideas related method of averaging. It is shown that in some parameter regions the systems exhibit harmonic solution bifurcation and subharmonic solution bifurcation. Furthermore, the stability of subharmonic solutions is discussed. |
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| Keywords: | Hopf bifurcation method of averaging harmonic solution bifurcation subharmonic solution bifurcation stability |
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