The attractor landscape of duplicated networks

We study the effect that network duplication has on the topology of the state space of dynamical Boolean networks with thresholds. We show that the problem of finding the attractor dynamics is just as hard as finding the attractors of the unduplicated network. We also show that a reverse algorithm –normally not computationally advantageous in determining the basins of attraction– can now exploit the symmetry of the system and its computational complexity does not scales exponentially anymore with the size of the network. Lastly, we show that when a chain of network duplication events is considered, only the first events change the nature of the attractors, while successive events only affect/reinforce the basins of attraction.