Redundancy and error resilience in Boolean Networks

We consider the effect of noise in sparse Boolean Networks with redundant functions. We show that they always exhibit a non-zero error level, and the dynamics undergoes a phase transition from non-ergodicity to ergodicity, as a function of noise, after which the system is no longer capable of preserving a memory if its initial state. We obtain upper-bounds on the critical value of noise for networks of different sparsity.