| 对称双弹簧振子系统的横振动的主共振与分岔 |
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| 引用本文： | 王立明.对称双弹簧振子系统的横振动的主共振与分岔[J].重庆科技学院学报(自然科学版),2010,12(1):180-182. |
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| 作者姓名： | 王立明 |
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| 作者单位： | 廊坊师范学院,廊坊,065000 |
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| 基金项目： | 河北省廊坊市科学技术与发展指导计划项目(No.2009011002) |
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| 摘 要： | 采用渐进法求近似解并用四阶Runge-Kutta法求数值解进行验证,分析和讨论了对称双弹簧振子受迫横振动周期解的多值性和振幅跳跃现象;绘制系统的分岔图研究系统拓扑结构随参数f0的变化,分析系统进入混沌的道路。结合对系统的Lyapunov指数、相轨图及Poincare映射的分析验证了上述结论,最后给出了系统的Lyapunov维数谱。
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| 关 键 词： | 渐近法 Runge-Kutta法 Lyapunov指数 分岔 Poincare映射 |
Primary Resonance and Bifurcation of the Forced Transverse Oscillation in the Symmetric Two-springed Oscillator |
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| WANG Li-ming.Primary Resonance and Bifurcation of the Forced Transverse Oscillation in the Symmetric Two-springed Oscillator[J].Journal of Chongqing University of Science and Technology:Natural Science Edition,2010,12(1):180-182. |
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| Authors: | WANG Li-ming |
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| Affiliation: | Langfang Teachers College;Langfang 065000 |
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| Abstract: | In this paper,the periodic solution to the forced transverse oscillation in the symmetric two-springed oscillator is acquired by means of approximate theory and testified with method of Runge-Kutta,the muti-value of periodic solution and the jumping of amplitude are discussed.In addition,by simulating the bifurcation diagrams,routes from double periodic bifurcation of periodic motion to chaos are discussed.At the same time,the conformity of the Lyapunov exponents and Lyapunov dimensions and bifurcation diag... |
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| Keywords: | means of approximate theory method of Runge-Kutta Lyapunov exponents bifurcation chaos Poincare map |
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