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Complex dynamical systems are prevalent in various domains, but theiranalysis and prediction are hindered by their high dimensionality andnonlinearity. Dimensionality reduction techniques can simplify the systemdynamics by reducing the number of variables, but most existing methods do notaccount for networked systems with separable coupling-dynamics, where theinteraction between nodes can be decomposed into a function of the node stateand a function of the neighbor state. Here, we present a novel dimensionalityreduction framework that can effectively capture the global dynamics of thesenetworks by projecting them onto a low-dimensional system. We derive thereduced system's equation and stability conditions, and propose an error metricto quantify the reduction accuracy. We demonstrate our framework on twoexamples of networked systems with separable coupling-dynamics: a modifiedsusceptible-infected-susceptible model with direct infection and a modifiedMichaelis-Menten model with activation and inhibition. We conduct numericalexperiments on synthetic and empirical networks to validate and evaluate ourframework, and find a good agreement between the original and reduced systems.We also investigate the effects of different network structures and parameterson the system dynamics and the reduction error. Our framework offers a generaland powerful tool for studying complex dynamical networks with separablecoupling-dynamics.

Dimensionality reduction of networked systems with separable coupling-dynamics: theory and applications