Distinguishing pairwise and higher-order interactions in coupled oscillators from time series

Rhythmic phenomena, which are ubiquitous in biological systems, are typically modeled as systems of coupled limit cycle oscillators. Estimating a mathematical model from experimental data is an essential step in understanding the dynamics of real-world complex systems. In coupled oscillator systems, identifying the type of interaction (e.g., pairwise or three-body) is challenging because different interactions can exhibit similar dynamical states in experimental conditions. In this study, we have developed a method based on the adaptive LASSO (Least Absolute Shrinkage and Selection Operator) to infer the interactions among oscillators from time series data. The proposed method successfully identifies the type of interaction and infer individual pairwise and three-body couplings. Through systematic analysis of synthetic datasets, we have demonstrated that our method outperforms two baseline methods, LASSO and OLS (Ordinary Least Squares), in accurately inferring the topology and strength of couplings between oscillators. Furthermore, the proposed method is applied to human brain network data, demonstrating its practical utility. Finally, we extend the method to more general oscillatory systems, including those exhibiting the deformation of limit cycles and those with four-body interactions. These results suggest that our method is a promising tool for identifying interaction mechanisms in oscillatory systems. Rhythmic phenomena, ubiquitous in biological systems, are often modeled as networks of coupled limit-cycle oscillators. This study introduces an adaptive LASSO based approach to infer the interaction type-"including pairwise and higher-order interactions-" from time-series data, demonstrating its effectiveness on synthetic datasets and human brain network data.