for details) and obtain a multivariate data $\{ y_1(t), y_2(t), \dots, y_N(t) \}$ for a time $T=5000$. For simplicity, we will denote $y_i = \{ y_i(t)\}_{t=0}^T$, whenever there is no risk of confusion.

For comparison, we first test the recovery of the network using the functional network framework [@bettinardi2017; @eguiluz2005; @bullmore2009]. The intuition behind this approach is that nodes with similar time series perform analogous functions in the network and are assumed to have similar characteristics. The functional network can thus be constructed by the matrix of the similarities between nodes via statistical analysis [@zhang2006; @greicius2003]. Here we employ a covariance analysis between the time series. The functional network alone does not detect communities from the data because the bursts are erratic (Fig. \[RC2\] (b)). Other similarity measures such as mutual information give no significative improvement.

We also compared our method with a reconstruction by the sparse recovery technique [@brunton2015; @wang2016]. There, the dynamics is written as linear combination of chosen basis functions and the unknowns are the coefficients. Sparse recovery works well when many coefficients are exactly zero. The presence of a link is determined when any coefficient of the corresponding interaction is nonzero. In our setting, each link 