# 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.