Reverse engineering of complex dynamical networks in the presence of time-delayed interactions based on noisy time series

摘要

Reverse engineering of complex dynamical networks is important for a varietyof fields where uncovering the full topology of unknown networks and estimatingparameters characterizing the network structure and dynamical processes are ofinterest. We consider complex oscillator networks with time-delayedinteractions in a noisy environment, and develop an effective method to inferthe full topology of the network and evaluate the amount of time delay basedsolely on noise- contaminated time series. In particular, we develop ananalytic theory establishing that the dynamical correlation matrix, which canbe constructed purely from time series, can be manipulated to yield both thenetwork topology and the amount of time delay simultaneously. Extensivenumerical support is provided to validate the method. While our method providesa viable solution to the network inverse problem, significant difficulties,limitations, and challenges still remain, and these are discussed thoroughly.