Network reconstruction based on generalized splay state

Abstract

Complex network is the simplest abstraction of the interaction of the components of the systems. Reconstructing the full topology of the network from data is a focal problem for understanding and controlling the dynamics behavior of the systems. Based on the characteristics of generalized periodic splay state of weakly coupled systems, that is, when the system is in the generalized periodic splay state, the nodes which are connected directly usually have different phases, and the phases of the nodes which are not connected directly are usually random, we develop an efficient approach to reconstruct the topology of complex network. With the most simplified form of Logistic map as the node dynamics of the coupled systems, we calculate the matrix of the phase correlation, and reconstruct the topological structure of the networks according to the matrix. It is found that this method can reconstruct the topological structure of the complex network with sparse connection perfectly.