| Duffing方程的分叉结构及其标度特性 |
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| 引用本文： | 朱顺泉,谢发根,胡岗.Duffing方程的分叉结构及其标度特性[J].物理学报,1992,41(10):1638-1646. |
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| 作者姓名： | 朱顺泉 谢发根 胡岗 |
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| 作者单位： | (1)北京师范大学物理系,北京100875; (2)北京师范大学物理系,北京100875;中国科学院理论物理研究所,北京100080; (3)西南师范大学物理系,重庆630175 |
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| 摘 要： | 对称三次幂的Duffing方程经标度变换可化为三参数方程。在小周期强迫力的条件下,负线性项的Duffing方程具有封闭的分叉结构,且分叉区域随着线性系数的增大而缩小。在大周期强迫力的条件下,方程具有一系列自相似分叉结构,并呈现标度特性,利用一维映射对此标度特性进行了讨论、理论结果与计算机结果符合很好。
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| 关 键 词： | 杜分方程 标度性 分叉结构 |
| 收稿时间： | 1991-10-17 |
BIFURCATION STRUCTURE AND SCALING PROPERTY OF DUFFING'S EQUATION |
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| ZHU SHUN-QUAN,XIE FA-GENG and HU GANG.BIFURCATION STRUCTURE AND SCALING PROPERTY OF DUFFING''S EQUATION[J].Acta Physica Sinica,1992,41(10):1638-1646. |
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| Authors: | ZHU SHUN-QUAN XIE FA-GENG and HU GANG |
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| Abstract: | Symmetric cubic Duffing's equation can be identified to three-parameter equation by using scaling transformation. Duffing's equation with, negative linear term has a closed bifurcation region under weak periodic force, the bifurcation areas contract with increasing the linear coefficient. The equation has a set of self-similar bifurcation regions under strong periodic force. The scaling property of this regions is found and discussed in terms of a one-dimensional map, the theoretical result is in good agreement with the computational result. |
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