Infering Underlying Networks from Time Series of Dynamical Systems and Evaluating Global Balance

Abstract

A complex system’s emerging behavior is a result of the interactions of its components. A graph-theoretic representation of it is a network of interactions dictating through differential equations the evolution of the state of the individual components, represented by nodes. These networks can be signed, directed, and weighted. Our first goal is to infer these networks of interactions from time series relying on dynamical systems theory. Our second goal is to characterize these networks, and for this purpose, we rely on multiscale definitions of the frustration indices. We implement algorithms that compute the indices of frustration on multiple levels, explore and address some of the computational bottlenecks, and apply the algorithms to the network inferred from the dynamics.