An Energy Based General Framework for Dynamical Complex Networks

Abstract

Complex networks are ubiquitous in nature. It is essential to understand the mechanism that defines network dynamics and constituent interaction. Defining network behaviors is challenging because network dynamics exist simultaneously at the microscopic (local) level and macroscopic (global) level. A proper description of the dynamics inherent of all complex networks is needed. This study addresses the need and develops a general framework for describing complex networks dynamics. The generality of the general framework is demonstrated using a 20-constituent point mass network and a 6-neuron brain network – examples from two different physical domains. The former is a real-life complex network that is exposed to environmental disturbance and undergoes constant change of network structure due to individual constituent joining and leaving the network. The dynamics of the 20-constituent network is a spatial translational network system whose dynamics is exhibited in the displacement and velocity of individual constituents. A multivariable time-frequency complex network control scheme is also applied to ensure the integrity of the network structure and its robustness to disturbance. The 6-neuron brain network is a complex network in the biology domain whose dynamics is dominated by magnetic flux and exhibited in the form of electrical voltage fluctuations of neuronal membrane.