Generative framework for dimensionality reduction of large scale network of nonlinear dynamical systems driven by external input

Abstract

Several studies have proposed constraints under which a low-dimensional representation can be derived from large-scale real-world networks exhibiting complex nonlinear dynamics. Typically, these representations are formulated under certain assumptions, such as when solutions converge to attractor states using linear stability analysis or using projections of large-scale dynamical data into a set of lower dimensional modes that are selected heuristically. Here, we propose a generative framework for selection of lower dimensional modes onto which the entire network dynamics can be projected based on the symmetry of the input distribution for a large-scale network driven by external inputs, thus relaxing the heuristic selection of modes made in the earlier reduction approaches. The proposed mode reduction technique is tractable analytically and applied to different kinds of real-world large-scale network scenarios with nodes comprising of (a) Van der Pol oscillators (b) Hindmarsh-Rose neurons. These two demonstrations elucidate how order parameter is conserved at original and reduced descriptions thus validating our proposition.