On the Efficacy of Information Transfer in Complex Networks
Authors: Shettigar Nandan , Yang Chun-Lin , Suh C. Steve 
Published: January 2022

Abstract
The adaptability of a complex network determines its ability to maintain stability in a time-dependent environment. These change in macrostate dynamics (time-varying properties in the form of adaptations) are facilitated through a respective change in the microstate configurations of a network. Consequently, these configurations are in terms of the cumulative interactions of the constituents which compose the network ensemble. The nonlinear culmination of these interactions (connections) result in emergent patterns. Therefore, defining the local degree of coupling (strength of connected interactions between constituents) and how these change over time is essential to determine the resultant global time-varying properties of a complex network. Thus, this study proposes the parameters of connectivity (degree of coupling) between constituents in terms of efficacy of information transmission and reception. The underlying logic is that the degree of coupling between two nodes (constituents) can be defined in terms of how much information is transmitted by a donor and how well this is received by the recipient. These parameters control the microstate configurations of a complex network from which macrostate dynamics emerges that govern the adaptability of the network. As global network dynamical properties are nonstationary, the individual (local) constituents and their couplings must also exhibit dynamic, nonstationary behaviors to maintain stability. These local factors result in highly nonlinear behaviors which produce an amalgamation of overall (global) synchronous and asynchronous emergent patterns based on a desired objective and physical system constraints. Furthermore, the intrinsically time-variant nature of the individual constituents and their connections have a particular degree of variance in the time and frequency domains. This characteristic of the degree of coupling controls and allows for change in the magnitude of information transfer between nodes (constituents) in the network. Thus, the adaptability of the degree of coupling and is the foundational basis that allows the global collective properties of a network system to have a high degree of adaptability and robustness to time-varying environments (external disruptions that can compromise system stability). Additionally, emergent behaviors result from the constructive (or destructive) interactions of local dynamics which can increase (or decrease) the influence of individual behaviors amidst the scales of a complex network. This produces a mix of global asynchronous and synchronous organization across spatial and temporal scales that correspond to stable ensemble behaviors. These spatiotemporal scales may exhibit statistical self-similarity. The specific type of emergent scales of behavior is regulated by the degree of coupling between constituents. Therefore, effectively regulating the degree of coupling between constituents is a fundamental basis in regulating a complex network’s capability to adapt to disturbances coming from within as well as without. General parameters defining the degree of coupling are the efficacy of information transmission and the efficacy of information reception. In this study, synaptic plasticity (the modulation of the degree of coupling between neurons) in the human brain is used as an example to enumerate how the parameters controlling the degree of coupling between nodes (the efficacy of information transmission and reception) can be defined, modeled and universally implemented to further a comprehensive understanding of the nonlinear and potential chaotic nature of complex networks in general.