Coupling functions: Universal insights into dynamical interaction mechanisms

The dynamical systems found in Nature are rarely isolated. Instead they\ninteract and influence each other. The coupling functions that connect them\ncontain detailed information about the functional mechanisms underlying the\ninteractions and prescribe the physical rule specifying how an interaction\noccurs. Here, we aim to present a coherent and comprehensive review\nencompassing the rapid progress made recently in the analysis, understanding\nand applications of coupling functions. The basic concepts and characteristics\nof coupling functions are presented through demonstrative examples of different\ndomains, revealing the mechanisms and emphasizing their multivariate nature.\nThe theory of coupling functions is discussed through gradually increasing\ncomplexity from strong and weak interactions to globally-coupled systems and\nnetworks. A variety of methods that have been developed for the detection and\nreconstruction of coupling functions from measured data is described. These\nmethods are based on different statistical techniques for dynamical inference.\nStemming from physics, such methods are being applied in diverse areas of\nscience and technology, including chemistry, biology, physiology, neuroscience,\nsocial sciences, mechanics and secure communications. This breadth of\napplication illustrates the universality of coupling functions for studying the\ninteraction mechanisms of coupled dynamical systems.\n