I am trying to extract the MSF (master stability function) for a network of chaotic Rössler systems. I am letting one subsystem to evolve to its chaotic attractor; then we have a trajectory $s(t)$. After the transient has died out, I take several random points on the attractor, e.g. ${s(t=100), s(t=200), ...}$ and insert $(x_s,y_s,z_s)$ into the variational equation: $$ \frac{\mathrm{d}}{\mathrm{d}t}\delta_i(t) = [\mathrm{D}F(s)-\alpha \mathrm{D}H(s)] \delta_i(t) $$
I then let this evolve for a rather large time and calculate its largest Lyapunov exponent via the orbit-separation method. At the end, I take the mean value to represent the largest Lyapunov exponent of the variational dynamics. So far, did I do right?
However, the negative region of the MSF does not agree with the ones I see in different papers. Any ideas what am I doing wrong?
You do not talk much about this step, so I cannot be sure, but you seem to be missing the transformations that allow to separate directions tangential and transversal to the synchronisation manifold. If you do not do this, you should always get a positive Lyapunov exponent due to the chaoticity of the Rössler system.