Next: Adaptation
Up: Hopf Continuation
Previous: Mathematical definition
  Contents
In continuous-time systems there are four generic codim 2 bifurcations that can be detected along the Hopf curve:
- Bogdanov - Takens. We will denote this bifurcation by BT
- Zero - Hopf point, denoted by ZH
- Double - Hopf point, denoted by DH
- Generalized Hopf point, denoted by GH
To detect these singularities, we first define 4 test functions:
- f1=k
-
f2=det(fu)
-
|
|
|
æ ç ç ç
ç ç è
|
é ê
ê ë
|
|
|
ù ú
ú û
|
\ |
æ ç ç ç
ç ç è
|
|
|
ö ÷ ÷ ÷
÷ ÷ ø
|
ö ÷ ÷ ÷
÷ ÷ ø
|
n+1
|
|
|
-
f4 = l1 (first Lyapunov coefficient).
In this case the singularity matrix is: