### Fold initialization

The most natural way to start a fold curve continuation in the toolbox is from a limit point. As in the case of equilibria, a fold curve continuation cannot be done by just calling the continuer as:
`[x,v,s,h,f]=cont(@limitpoint, x0, v0, opt)`.
The fold curve file has to know

- which odefile to use,
- which parameters are active,
- the values of all parameters.

To initialize the continuation one first gives the following command:
`[x0,v0]=init_LP_LP(@odefile, xnew, p, ap )`.

In this command `xnew` must be a vector that contains the values of the state variables. `p` must contain the current values of all the parameters and `ap` must be the indices of the active parameters. In the most natural situation where `x` is the matrix returned by the previous equilibrium curve continuation one starts to build by the command `xnew=x(1:nphase,s(i).index)`, where `nphase` is the number of state variables and `s(i)` is the special point structure of the detected fold point on the equilibrium curve continuation. Next, the command `p(ap_old)=x(end,s(i).index);` replaces the old value of the free parameter in the previous run by the newly found parameter `p`. `odefile` specifies the ode-file to be used. `bp` are the optional indices of the branch parameters. It also works without entering a value for this field.

MATCONT provides four other initializers which allow to continue a fold curve from a codim 2 equilibrium bifurcation, namely `init_BP_LP.m,` `init_BT_LP.m,` `init_CP_LP.m` and `init_ZH_LP.m`. In fact, these initializers are only added for ease of use: they refer back to `init_LP_LP.m.`