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In the MatCont / CL_MatCont toolbox Hopf curves are computed by minimally extended defining systems,
cf. [9] § 4.3.4.
The Hopf curve is defined by the following system
with the unknowns u,a,k,(i1,j1,i2,j2) Î {1,2} and where g=(
) is obtained by solving
|
æ ç
ç è
|
|
ö ÷
÷ ø
|
|
æ ç
ç è
|
|
ö ÷
÷ ø
|
= |
æ ç
ç è
|
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ö ÷
÷ ø
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, |
| (64) |
where fu has eigenvalues ±iw,w > 0, k=w2 and
Vbor,Wbor Î Rn×2 are chosen such that the matrix in
(64) is nonsingular. i1,j1,i2,j2,Vbor and Wbor are auxiliary
variables that can be adapted.
This method is implemented in the curve definition file hopf.m.