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Bifurcations

In continuous-time systems there are four generic codim 2 bifurcations that can be detected along the Hopf curve:

To detect these singularities, we first define 4 test functions:

In this case the singularity matrix is:

S = æ
ç
ç
ç
ç
ç
è
0
0
-
-
1
0
-
-
-
-
0
-
-
-
-
0
ö
÷
÷
÷
÷
÷
ø
(65)