Microscopic interactions lead to mutual synchronization in a network of networks

This Letter proposes a stochastic coupling scheme to study the collective dynamics in a network that comprises random Boolean networks. Based on microscopic interactions, which are understood as the exchange of information among nodes, mutual synchronization can be achieved when the product of the assigning probability and influence probability exceeds a critical threshold. A mean field model is developed to approximate the dynamical behaviors of the original system. The effect of finite system size can be further mimicked by incorporating a noise term into the model. The dependence of the synchronization threshold on the degrees of connectivity and coupling configuration is analyzed.

► A coupling scheme is proposed to investigate the dynamics in a network of networks.
► Mutual synchronization can be achieved in the studied system.
► A mean field model is formulated to approximate the revealed dynamics.
► Synchronization threshold depends on the degree of connectivity and system size.