# From codim 2 to periodic orbits

## From Bautin point to curve Folds of periodic orbits

From the Bautin normal form, we know that there is a curve of Fold of periodic orbits near the bifurcation point.

We provide an automatic branch switching method in this case which reads as follows:

```
continuation(br::HopfCont, ind_BAUTIN::Int,
_contParams::ContinuationPar,
prob::AbstractPeriodicOrbitProblem ;
δp = nothing, ampfactor = 1, kwargs...)
```

where `prob`

is a method to compute periodic orbits (see From Hopf point to periodic orbits for more information).

Note that the two parameters in `br`

will be used for the continuation of Fold points of periodic orbits.

See ODE for an example of use.

## From Zero-Hopf (ZH) point to curve NS of periodic orbits

From the Zero-Hopf normal form, we know that there is a curve of Neimark-Sacker (NS) bifurcations of periodic orbits near the bifurcation point.

We provide an automatic branch switching method in this case which reads as follows:

```
continuation(br::TwoParamCont, ind_ZH::Int,
_contParams::ContinuationPar,
prob::AbstractPeriodicOrbitProblem ;
δp = nothing, ampfactor = 1, kwargs...)
```

where `prob`

is a method to compute periodic orbits (see From Hopf point to periodic orbits for more information).

Note that the two parameters in `br`

will be used for the continuation of NS points of periodic orbits.

## From Hopf-Hopf (HH) point to curve NS of periodic orbits

From the Hopf-Hopf normal form, we know that there are two curves of Neimark-Sacker (NS) bifurcations of periodic orbits near the bifurcation point.

We provide an automatic branch switching method in this case which reads as follows:

```
continuation(br::TwoParamCont, ind_HH::Int,
_contParams::ContinuationPar,
prob::AbstractPeriodicOrbitProblem ;
δp = nothing, ampfactor = 1,
whichns = 1,
kwargs...)
```

where `prob`

is a method to compute periodic orbits (see From Hopf point to periodic orbits for more information). The option `whichns`

which belongs to {1,2} controls which NS curve you want to compute.

Note that the two parameters in `br`

will be used for the continuation of NS points of periodic orbits.

See ODE for an example of use.