Modeling and analysis of evolving complex systems based on temporal networks

Abstract

Many complex systems evolve in time, and temporal networks are a useful framework to represent and analyze their components' dynamic interactions. Analyzing empirical temporal networks, we quantify essential features in the interaction patterns and propose two kinds of temporal network models to describe the interaction mechanism. One focuses on heterogeneous nodal activities and linking memory. Through this model, we discuss the structural and temporal properties, such as degree distribution and aging effect, according to activity distributions, memory exponents, and time resolutions. We also investigate the role of activity and memory in dynamic processes such as epidemic and random walk (RW) processes. In particular, we propose a finite-size scaling function for the coverage of the RW process. Based on the temporal percolation concept, we derive scaling exponents in the dynamics of the largest cluster and the coverage of the RW process. In addition, we conjecture the extended finite-size scaling ansatz for dynamic topologies and the fundamental property of temporal networks, which are numerically confirmed. The other model considers periodic collective effects and non-random interaction process. Using this model, we investigate the effects of time-varying environments and node-to-node interactions in network dynamics, and show that long-range temporal correlations can exist in the collective dynamics of interactions caused by them. Our researches provide a comprehensive picture of the dynamic topologies of temporal networks as well as temporal interaction patterns.