Title: Coupling functions: Universal insights into dynamical interaction mechanisms,
Abstract: The dynamical systems found in Nature are rarely isolated. Instead they
interact and influence each other. The coupling functions that connect them
contain detailed information about the functional mechanisms underlying the
interactions and prescribe the physical rule specifying how an interaction
occurs. Here, we aim to present a coherent and comprehensive review
encompassing the rapid progress made recently in the analysis, understanding
and applications of coupling functions. The basic concepts and characteristics
of coupling functions are presented through demonstrative examples of different
domains, revealing the mechanisms and emphasizing their multivariate nature.
The theory of coupling functions is discussed through gradually increasing
complexity from strong and weak interactions to globally-coupled systems and
networks. A variety of methods that have been developed for the detection and
reconstruction of coupling functions from measured data is described. These
methods are based on different statistical techniques for dynamical inference.
Stemming from physics, such methods are being applied in diverse areas of
science and technology, including chemistry, biology, physiology, neuroscience,
social sciences, mechanics and secure communications. This breadth of
application illustrates the universality of coupling functions for studying the
interaction mechanisms of coupled dynamical systems.