Universal transient behavior in large dynamical systems on networks
Wojciech Tarnowski, Izaak Neri, Pierpaolo Vivo · Physical Review Research · 2020
This paper develops an exact formalism to study how network architecture influences the transient dynamics of large dynamical systems in the vicinity of a stationary point. It is shown that for unidirectional networks the average dynamical response to initial perturbations is universal and only depends on a single parameter, encoding the average interaction strength between the individual constituents. Results are illustrated with numerical simulations on random graphs and real-world graphs, including a foodweb and a signalling network.