Perturbation propagation in random and evolved Boolean networks

In this paper, we investigate the propagation of perturbations in Boolean networks by evaluating the Derrida plot and its modifications. We show that even small random Boolean networks agree well with the predictions of the annealed approximation, but nonrandom networks show a very different behaviour. We focus on networks that were evolved for high dynamical robustness. The most important conclusion is that the simple distinction between frozen, critical and chaotic networks is no longer useful, since such evolved networks can display the properties of all three types of networks. Furthermore, we evaluate a simplified empirical network and show how its specific state space properties are reflected in the modified Derrida plots. 3 Author to whom any correspondence should be addressed. New Journal of Physics 11 (2009) 033005 1367-2630/09/033005+13$30.00 © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft