## Equilibrium initialization

Naively, one would start the continuation immediately with:

> `[x,v,s,h,f]=cont(@equilibrium, x0, v0, opt)`

However, the equilibrium curve file has to know :

- which ode file to use,
- the values of all state variables,
- the values of all parameters,
- which parameter is active.

All this information can be supplied by one of the following two starting functions. Both functions return an initial point `x0` as well as its tangent vector `v0`.

- `[x0,v0]=init_EP_EP(@odefile, x, p, ap)`

  This routine stores its information in a global structure `eds` (see also Figure 4). The result of `init_EP_EP` is a vector `x0` with the state variables and the active parameter and a vector `v0` that is empty. Here `odefile` is the ode-file (system-definition file) to be used, `x` is a vector containing the values of the state variables. `p` is the vector containing the current values of the parameters and `ap` is the active parameter. The full listing of the equilibrium initializer can be found in the file 'Equilibrium/init_EP_EP.m' of the toolbox.

- `[x0,v0]=init_BP_EP(@odefile, x, p, s, h)`

  Calculates an initial point for starting a new branch from a branch point detected on an equilibrium curve. This routine stores its information in a global structure `eds` (see also Figure 4). Here `odefile` is the ode-file (system-definition file) to be used, `x` is a vector containing the values of the state variables returned by a previous equilibrium curve continuation. `p` is the vector containing the current values of the parameters and `h` contains the value of the initial amplitude. The full listing of the equilibrium initializer and the curve definition can be found in the files 'Equilibrium/init_BP_EP.m' and 'equilibrium.m' of the toolbox, respectively.