Identifying structures of continuously-varying weighted networks

Identifying network structures from dynamical observations is a fundamental problem currently pervading scientific research on complex systems, as understanding and modeling the structure of a complex network will lead to greater knowledge of its evolutionary mechanisms and to a better understanding of its functional behaviors. Usually, one needs to identify a network's structure through a limited number of observations. Particularly, couplings of many real-world networks are sparse and continuously varying with time. In this study, a new framework is developed via optimization for identifying structures of continuously-varying weighted networks formed by sparsely-connected dynamical systems. Furthermore, a regularization technique is employed to increase the numerical stability of the parameter estimation algorithm. Three numerical examples are provided to illustrate the feasibility and effectiveness of the proposed identification method. In comparison with other existing techniques, the main advantages of our method include its ability to identify structures of continuously-varying weighted networks in addition to static ones, as well as its requirement of a relatively small number of observations. The proposed method has a potential applicability to a variety of evolving complex dynamical networks.