The figure 3.6 allows us to have a more syntetic vue of the bifurcations of the KSE.

In fact, I have seen that, even if for low value of , the theoretical study can predict the dynamic of the Kuramoto-Sivashinsky, the more increase, the more complex the dynamic is. The dynamic of the KSE is a big problem because this equation is representative of lot of phenomenon like :

- chemical oscillation or chemical fronts
- flame front in combustion
- numerical dissipation

Moreover, for the course of hydrodynamic instabilities, this equation was very interesting. This project allows me to see the applications of this course and make me work on a important part of my formation : the numerical methods.