# Periodic orbits computation

Consider the DDE problem written

\[\frac{du}{dt}=F(u(t), u_t;p).\tag{E}\]

A periodic solution $u^*$ with period $T$ satisfies $u^*(t+T)=u^*(t)$ for all time $t$.

We provide 1 method for computing periodic orbits (PO):

- one (Collocation) based on orthogonal collocation to discretize the above problem (E),

## Important notes

We regroup here some important notes which are valid for all methods above.

### 1. Finaliser

If you pass a `finalize`

function to continuation, the following occurs:

- If the newton solve was successfull, we update the phase condition every
`update_section_every_step`

- we call the user defined finalizer
`finalize`

.