Relying only on nonlinear collective dynamics, our Algorithm for Revealing Network Interactions (ARNI) reveals the interaction topology of networks without neither assuming specific dynamic models to be known in advance nor assuming the dynamics admits sparse representations, nor imposing controlled drivings on the network. Furthermore, ARNI works reliably across many dynamical regimes, including transient dynamics toward steady states, periodic and non-periodic dynamics, and chaos. Together with its capabilities to reveal network (two point) as well as hyper-network (e.g., three point) interactions, this framework may thus open up nonlinear dynamics options of inferring direct interaction patterns across systems where no model is known.

We provide example codes and functions in MATLAB for reconstructing different models of network dynamical systems exhibiting diverse dynamical regimes such as transient dynamics towards steady state, non-periodic dynamics and chaos.

Concerning the models employed for simulating the time series, we employ (i) two different models for phase-coupled oscillators differing in complexity, (ii) a model mimicking the transient dynamics of gene circuits, and (iii) coupled-Roessler oscillators operating in a chaotic regime.

Installation consists in extracting the entire zip file ARNI_Matlab.zip in a local folder. Running the examples is as simple as running the corresponding .m files.

Further documentation may also be found in Casadiego et al., Nature Communications 8 (2017).