Next: Bifurcations Up: Branch Point Continuation Previous: Branch Point Continuation   Contents

Mathematical definition

In the toolbox branch point curves are computed by minimally extended defining systems, cf. [27], § 4.1.2. The branch point curve is defined by the following system

ì
ï
í
ï
î
f(u,a)
=
0,
g1(u,a)
=
0,
g2(u,a)
=
0,
(83)

where (u,a) Î Rn+2, while g1 and g2 are obtained by solving

N4 æ
ç
ç
ç
è
v11
v21
v12
v22
g1
g2
ö
÷
÷
÷
ø
= æ
ç
ç
ç
è
0n
0n
1
0
0
1
ö
÷
÷
÷
ø
.
(84)

Here v11 and v21 are functions and v12,v22,g1 and g2 are scalars and

N4 = é
ê
ê
ê
ë
fu(u,a)
fb(u,a)
w01
v011T
v012T
0
v021T
v022T
0
ù
ú
ú
ú
û

where the bordering functions v011,v021,w01 and scalars v012,v022 are chosen so that N4 is nonsingular. This method is implemented in the curve definition file branchpoint.m.