Duffing方程的分叉结构及其标度特性  

BIFURCATION STRUCTURE AND SCALING PROPERTY OF DUFFING'S EQUATION

作　　者：朱顺泉[1] 谢发根 胡岗[2] 

机构地区：[1]西南师范大学物理系,重庆630175 [2]北京师范大学物理系,北京100875

出　　处：《物理学报》1992年第10期1638-1646,共9页Acta Physica Sinica

基　　金：国家自然科学基金

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。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.

关 键 词：杜分方程 标度性 分叉结构 

分 类 号：O32[理学—一般力学与力学基础]