Time-delayed Network Reconstruction based on Nonlinear Continuous Dynamical Systems

Abstract

Time-delayed interactions are of vital importance in analysis and control of real networked systems. As for the limited noisy observations, data-driven modeling of these complex time-delayed systems is a central and challenging topic in numerous fields of science and engineering. Due to nonuniform lags usually embedded in the real-world systems, the inclusion of all lagged components would result in the false causal analysis. In this paper, based on data-fusion strategy, we put forward a novel approach for identifying nonlinear continuous time-delayed dynamical systems with nonuniform lags, termed Feature Selection Nonlinear Conditional Granger Causality (FSNCGC). In detail, rather than treating all the lagged components equally, we present a feature selection method based on information theory to select the candidate lagged components of driving variables, which minimizes the criterion of the mean conditional mutual information between unselected lagged components and target variable. Moreover, for each target variable, we just consider the specific selected lagged components for nonlinear conditional Granger causal analysis with F-test judgement. Finally, we apply our proposed method to a canonical nonlinear continuous time-delayed dynamical system. All of the results demonstrate that our proposed method performs well and provides a viable perspective for time-delayed network reconstruction.