Inferring connectivity of an oscillatory network via the phase dynamics reconstruction

Abstract

We review an approach for reconstructing oscillatory networks’ undirected and directed connectivity from data. The technique relies on inferring the phase dynamics model. The central assumption is that we observe the outputs of all network nodes. We distinguish between two cases. In the first one, the observed signals represent smooth oscillations, while in the second one, the data are pulse-like and can be viewed as point processes. For the first case, we discuss estimating the true phase from a scalar signal, exploiting the protophase-to-phase transformation. With the phases at hand, pairwise and triplet synchronization indices can characterize the undirected connectivity. Next, we demonstrate how to infer the general form of the coupling functions for two or three oscillators and how to use these functions to quantify the directional links. We proceed with a different treatment of networks with more than three nodes. We discuss the difference between the structural and effective phase connectivity that emerges due to high-order terms in the coupling functions. For the second case of point-process data, we use the instants of spikes to infer the phase dynamics model in the Winfree form directly. This way, we obtain the network’s coupling matrix in the first approximation in the coupling strength.

The time-evolving epileptic brain network: concepts, definitions, accomplishments, perspectives

“…The latter ansatz is often pursued in cases where a perturbation-based approach ( actio est reactio ) is either unfeasible or not constructive. Properties of an interaction can then be estimated with diverse linear and nonlinear, bi- and multivariate time-series-analysis techniques grounded in statistics ( Rodgers and Nicewander, 1988 ; Hamilton, 2020 ), nonlinear dynamics ( Kantz and Schreiber, 2003 ; Datseris and Parlitz, 2022 ), synchronization theory ( Arnhold et al, 1999 ; Pikovsky et al, 2001 ; Stankovski et al, 2012 ; Rosenblum and Pikovsky, 2023 ), statistical physics ( Tabar, 2019 ), and information theory ( Hlaváčková-Schindler et al, 2007 ), among others.…”