Order–disorder transition in the Chialvo–Bak ‘minibrain’ controlled by network geometry

We examine a simple biologically motivated neural network, the three-layer version of the Chialvo–Bak ‘minibrain’ (Neurosci. 90 (1999) 1137), and present numerical results which indicate that a non-equilibrium phase transition between ordered and disordered phases occurs subject to the tuning of a control parameter. Scale-free behaviour is observed at the critical point. Notably, the transition here is due solely to network geometry and not any noise factor. The phase of the network is thus a design parameter which can be tuned. The phases are determined by differing levels of interference between active paths in the network and the consequent accidental destruction of good paths.