Controlling of nonlinear dynamical networks based on decoupling and re-coupling method

Although a large number of studies have verified and explained the controllability of complex networks in real life and nature, there is a deficiency of accurate control strategies based on the proposed theory of network controllability. Here, we propose a new dimension reduction method, which firstly decouples the N-dimensional interdependent system into N independent systems, then re-couples them into one state space. The tool can help predict the state of individual nodes, explore the behavior pattern of different dynamic models in the network, and quantify the responses of the network states in terms of its own structure and external disturbances. The results show that for nonlinear dynamical models with biochemical dynamics, birth–death processes, regulatory dynamics and epidemic processes on Scale-Free and Erdös–Rényi networks, the activity of the target node or target node set can be accurately reached by controlling the behavior of some nodes with our framework.