CALCULATING NORMAL FORMS FOR NONSEMI SIMPLE BIFURCATIONS
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摘要: 在文［１］基础上，提出一种仅知道派生线性系统零实部特征值时求解非线性系统非半单分叉ＮｏｒｍａｌＦｏｒｍ的方法．通过适当的分类，将要求解的线性代数方程组分为若干相互独立的方程组．将所求系数向量按字典序列排列后，各独立方程组的系数矩阵是上三角矩阵．在非共振情形，各系数向量可按反字典序列递推求出．在共振情形，根据文中的二个定理，巧妙地由一简单的常数矩阵的最大秩子矩阵，定位其系数矩阵的满秩子矩阵，解决了这类方程组的降维简化．通过消元法，把简化后的方程化成类似于半单分叉ＮｏｒｍａｌＦｏｒｍ求解过程中方程的形式，其解法也类似．该方法非常易于在计算机代数软件平台上程序化．
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关键词:
- NormalForm /
- 非半单分叉 /
- 最大秩
Abstract: This paper presents a new scheme of calculating the Normal forms of a set of nonlinear ordinary differential equations when a nonsemi simple bifurcation occurs, with only the eigenvalues of zero real parts of the linearized differential equations given. It is well known that the classical matrix method enables one to establish the algebraic equations that govern the coefficients in the Normal form of a set of ordinary differential equations. However, it offers neither general technique of reducing the max...-
Key words:
- Normal form /
- nonsemi simple bifurcation /
- maximum rank
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