Before presenting this new bifurcation, I would like explain the way I
have realised the simulation. If I had start all the simulation with a
small perturbation, the time of calculation would have been too long. That's
why I use for the initialisation of the simulation for
the solution converged for .
With this strategy, it's easier to obtain the new convergence.
When the parameter
rich the value ,
the simulation converged toward a solution which looks like those of the
first bifurcation, but the difference is that this solution is travelling
on the domain. The speed of the solution is constant and increase with .
The animation below show the travilling wave for .
The graph of norm versus time is on the figure 3.3.
We can remark that the norm is not a constant. It's due to a numerical
problem, but it is not important to understand the phenomenon. Moreover
it allows us to calculate the speed of the wave. In fact the periodicity
of the norm is directly link to the speed of wave.
Figure 3.3: Norm versus time for