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| 基于近哈密顿系统的Hopf分岔 | |
| 引用本文： | 王桥医,徐先懂,唐文评.基于近哈密顿系统的Hopf分岔[J].中南大学学报(自然科学版),2004,35(2):258-261. |
| 作者姓名： | 王桥医 徐先懂 唐文评 |
| 作者单位： | 1. 株洲工学院,机械系,湖南株洲,412008;中南大学,机电工程学院,湖南长沙,410083 2. 中南大学,机电工程学院,湖南长沙,410083 3. 株洲工学院,机械系,湖南株洲,412008 |
| 基金项目： | 湖南省重点学科建设项目(2002 06)，湖南省教育厅科学研究项目(02C658) |
| 摘 要： | 针对三维时变小扰动哈密顿系统的Hopf分岔的理论仅仅适用于自治系统的情况,运用Melnikov方法研究了时变小扰动哈密顿系统周期轨道发生Hopf分岔的条件,并将这些条件应用于一类三维时变小扰动非自治系统,使之能用于非自治系统。研究结果表明,所研究的系统还存在复杂而有规律的环面分岔行为。 |
| 关 键 词： | 非线性动力学 小扰动 时变 哈密顿系统 Melnikov方法 Hopf分岔 |
| 文章编号： | 1672-7207(2004)02-0258-04 |
| 修稿时间： | 2002年10月6日 |
Hopf bifurcation based on a three-dimensional and time-dependent perturbation Hamiltonian system |
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| WANG Qiao-yi.Hopf bifurcation based on a three-dimensional and time-dependent perturbation Hamiltonian system[J].Journal of Central South University:Science and Technology,2004,35(2):258-261. | |
| Authors: | WANG Qiao-yi |
| Institution: | WANG Qiao-yi~ |
| Abstract: | This paper develops a new method to study the Hopf bifurcations of periodic orbits in three-dimensional, time dependent perturbation of planar Hamiltonian differential equations, and gets a series of concise formula to simplify the Hopf bifurcation conditions by some mathematical skill and subharmonic Melnikov method. The Hopf bifurcation existence parameter domains described in an equation is deduced, elliptic functions and elliptic integration are used to calculate these parameter domains. In order to verify the method, the system is integrated at the bifurcation existence parameter domains with numerical method. The results indicate that the method is well coincided with the numerical results.Further numerical integration indicates that more complicated torus bifurcation exist in the example system. |
| Keywords: | nonlinear dynamics perturbation time-dependent Hamiltonian system Melnikov method Hopf bifurcation |
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