Network Stability, Realisation and Random Model Generation

Dynamical structure functions (DSFs) provide means for modelling networked dynamical systems and exploring interactive structures thereof. There have been several studies on methods/algorithms for reconstructing (Boolean) networks from time-series data. However, there are no methods currently available for random generation of DSF models with complex network structures for benchmarking. In particular, it may be desirable to generate "stable" DSF models or require the presence of feedback structures while keeping topology and dynamics random up to these constraints. This work provides procedures to obtain such models. On the path of doing so, we first study essential properties and concepts of DSF models, including realisation and stability. Then, the paper suggests model generation algorithms, whose implementations are now publicly available.