Computation of multiple pitchfork bifurcation points

被引:0
|
作者
Ponisch, G
Schnabel, U
Schwetlick, H
机构
来源
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK | 1997年 / 77卷
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D O I
暂无
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
A point (x*,lambda*) is called a pitchfork bifurcation point of multiplicity p greater than or equal to 1 of the nonlinear system F(z, lambda) = 0, F : R-n x R-1 --> R-n, if rank partial derivative(s)F(x*, lambda*) = n - 1 and if the Ljapunov-Schmidt reduced equation has the normal form g(xi, mu) = +/- xi(2+p) +/- mu xi = 0. It is shown that such points satisfy a minimally extended system G(y) = 0, G : Rn+2--> Rn+2 the dimension n + 2 of which is independent of p. For solving this system, a two-stage Newton-type method is proposed. Numerical tests show the influence on the convergence behavior of the starting point and of the bordering vectors used in the definition of the extended system.
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收藏
页码:S449 / S452
页数:4
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