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. A coherent and comprehensive review is presented 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.

Neuronal firing and DNA dynamics in a neural network

“…DNA is a thread-like chain of nucleotides carrying the genetic information used in the growth, development, functioning and reproduction of all known living organisms and many viruses. During the last decades, neuronal activity and DNA dynamics [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48] have received much interest because of their implications in most biological processes governing the behavior of all living cells, animals and plants.…”

Trend of Random Events in Organizing When Influenced by a Non-Observable Factor

“…In traditional analyzes, the samples in a multifactorial statistical analysis associated with Fuzzy Logic have scopes in which there is a wide variance distribution of the analyzed variables [4] [11], however, the internal movement that occurs between one variable and another, in terms of its interactions is not observed, but by the final sample data set and the use of mathematical tools that do not explain the relation between the parts of the samples from that point of view [12]. This form of analysis is not sufficient to visualize cause and effect relationships in the entanglement of event variables and their dynamics in modifying in time [13] when taking in account the matter and energy quantitative physical aspects of influence. Traditional methodological procedures of non-linear statistics verify only a portion of the state of nature of the event [12].…”

“…Traditional methodological procedures of non-linear statistics verify only a portion of the state of nature of the event [12]. Statistical models that analyze complex events usually bring to light, indicators determined to give the researcher the global view of a system in a functional state of complexity restricted to a certain space and time [13]. It can happen of correspondences among ana- The discussion proposed in this paper has as its basic premise the idea that the oscillations in an event tend to be delimitated by an unobservable factor, and must have an organization in which the probable is set to happen towards any sort of the given possibilities based on the quantitative physical aspects of the event.…”

Origin of Hyperbolicity in Brain-to-Brain Coordination Networks

“…To contribute to the efficient flow of information different brain regions continuously communicate with one another, resulting in synchronous fluctuations within characteristic frequency intervals. For this reason, the underlying functional mechanisms can be probed effectively by coupling functions [32], which accurately describes the paths to and from the synchronization [33]. In the case of brain-to-brain coordination networks, the links are emanating from the dynamics-correlations among EEG signals in various pairs of channels across two brains [4].…”