Chaos synchronization of two stochastically coupled random Boolean networks

In this Letter, we study the chaos synchronization of two stochastically coupled random Boolean networks (RBNs). Instead of using the “site-by-site and all-to-all” coupling, the coupling mechanism we consider here is that: the nth cell in a network is linked by an arbitrarily chosen cell in the other network with probability ρ  , and it possesses no links with probability 1−ρ1−ρ. The mechanism is useful to investigate the coevolution of biological species via horizontal genetic exchange. We show that the density evolution of networks can be described by two deterministic coupled polynomial maps. The complete synchronization occurs when the coupling parameter exceeds a critical value. Moreover, the reverse bifurcations in inhomogeneous condition are observed and under our discussion.