Pairwise vs Higher-order interactions: Can we identify the interaction type in coupled oscillators from time series?

Rhythmic phenomena, which are ubiquitous in biological systems, are typically modelled as systems of coupled limit cycle oscillators. Recently, there has been an increased interest in understanding the impact of higher-order interactions on the population dynamics of coupled oscillators. Meanwhile, estimating a mathematical model from experimental data is a vital 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) of a network is challenging, because different interactions can induce similar dynamical states and bifurcations. In this study, we have developed a method based on the adaptive LASSO (Least Absolute Shrinkage and Selection Operator) to infer the interactions between the oscillators from time series data. The proposed method can successfully classify the type of interaction and infer the probabilities of the existence of 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. Finally, we demonstrate the effectiveness of the proposed method by applying it to the synthetic data of 100 oscillators. These results imply that the proposed method is promising for identifying interactions from rhythmic activities in real-world systems.