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Thrid bifurcation
A thrid bifurcation happend when
become greater than approximatively.
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 .
The graph of norm versus time is on the figure 3.4.

Figure 3.4: Norm versus time for
The norm is periodic, even if we can see some differences between amplitudes
which are the consequences of the numerical scheme.
Julien Delbove
20001123