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Thrid bifurcation

A thrid bifurcation happend when $ \nu $ become greater than approximatively$ 160$. I have seen this bifurcation because after this value the amplitude of the norm which was the same for all the TW, begin to increase. The simulation are very long to obtain a converged solution. It's the reason why, in this domain the values of the norm I found, are certainly not good.

This bifurcation is a new loose of symetry. The solutions are travelling and oscillating. They are call Oscillating travelling wave. The animation shows a period of the solution for $ \nu = 175$.

The graph of norm versus time is on the figure 3.4.

\includegraphics [scale=0.8]{norm175.eps}
Figure 3.4: Norm versus time for $ \nu = 175$
The norm is periodic, even if we can see some differences between amplitudes which are the consequences of the numerical scheme.

Julien Delbove