Dimensionality reduction in discrete-time dynamical systems

Dimensionality reduction is a popular strategy for studying complex dynamical systems, especially high-dimensional networked systems. Its goal to discover more compact version of the system that retains almost important characteristics original and offers insights into inner functioning as well long-term behavior. However, because interaction structures, parameter configurations, initial conditions, etc., it still one open challenges in theory nonlinear science, present approaches are only relevant continuous-time format. Here, we an analytical framework reducing N-dimensional discrete-time S+1-dimensional effective function S parameters where much less than N. In particular, quantitative prediction dimensionality quality proposed. To demonstrate excellent performance our framework, test on variety challenging real-world Our study presents tool reduce systems can be applied wider range dynamic