In continuous-time systems there are four generic codim 2 bifurcations that can be detected along the fold curve:
To detect these singularities, we first define bp+3 test functions, where bp is the number of branch parameters:
In these expressions v,w are the vectors computed in (59) and(60) respectively, and
bi (branch parameters) are components of a.
The singularity matrix for bp=0 is:
| (61) |
The number of branch parameters is not fixed. If the number of branch parameters is 2 then this matrix has two more rows and columns. This singularity matrix is automatically extended:
|