| Duffing振子混沌动力学研究 |
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| 引用本文： | 王艳群.Duffing振子混沌动力学研究[J].衡阳师范学院学报,2007,28(3):33-35. |
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| 作者姓名： | 王艳群 |
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| 作者单位： | 衡阳师范学院数学系,湖南衡阳,421008 |
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| 基金项目： | 衡阳师范学院校科研和教改项目 |
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| 摘 要： | 研究了Duffing振子的混沌动力学。应用直接微扰法,我们构造了一级方程的通解,理论分析显示该通解的有界性条件包含着Melnikov混沌判据。当系统不满足微扰条件时,数值模拟表明随着外驱动力幅值增大,系统经历了一个倍周期分叉到混沌的过程。我们还发现,调节相关参数,可以有效的抑制系统的混沌。
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| 关 键 词： | Duffing振子 通解 Melnikov函数 倍周期分叉 混沌 |
| 文章编号： | 1673-0313（2007）03-0033-03 |
| 收稿时间： | 2006-11-07 |
| 修稿时间： | 2006-11-07 |
Studies of Chaotic Dynamics of A Duffing Oscillator |
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| WANG Yan-qun.Studies of Chaotic Dynamics of A Duffing Oscillator[J].journal of Hengyang Normal University,2007,28(3):33-35. |
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| Authors: | WANG Yan-qun |
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| Institution: | Department of Mathematics, Hengyang Normal Univevsity, Hengyang Hunan 421008, China |
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| Abstract: | This paper studies the chaotic dynamics of a Duffing oscillator.By using the direct perturbation method,we construct the general solution of the 1st-order equation.Theoretical analysis reveals that the boundedness condition of the general solution contains the Melnikov chaotic criterion.When the system cannot meet the perturbation conditions,numerical simulations show that,whith the increase in the amplitude of the external forcing,the system undergoes a process from period doubling to chaos.We also find that the chaos of the system canbe effectively suppressed by adjusting some parameters. |
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| Keywords: | Duffing oscillator general solution Melnikov function period doubling chaos |
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