Structure and dynamics of complex systems

Abstract

Interaction among many simple and identical elements as well as selective and nonlinear communication of different multifunctional elements with others leads to the system`s complex and coherent behavior. In past decades, greatly many works have been devoted to describe and characterize such complex systems. In particular, complex network theory and nonlinear dynamics are essential to figuring out structure and dynamics of complex systems, and are the key tools employed in this dissertation. Sampling of complex networks. In complex scale-free networks, ranking the individual nodes based upon their importance has useful applications, such as the identification of hubs for epidemic control, or bottlenecks for controlling traffic congestion. However, in most real situations, only limited sub-structures of entire networks are available, and therefore the reliability of the order relationships in sampled networks requires investigation. With a set of randomly sampled nodes from the underlying original networks, we ranked individual nodes by three centrality measures: degree, betweenness, and closeness. The higher-ranking nodes from the sampled networks provided a relatively better characterization of their ranks in the original networks than the lower-ranking nodes. A closeness-based order relationship was more reliable than any other quantity, due to the global nature of the closeness measure. In addition, we showed that if access to hubs is limited during the sampling process, an increase in the sampling fraction can in fact decrease the sampling accuracy. Finally, an estimation method for assessing sampling accuracy was suggested. Pattern formation of coupled oscillators. We investigated the dynamics of a two-dimensional array of oscillators with phase-shifted coupling. Each oscillator was allowed to interact with its neighbors within a finite radius. The system exhibits various patterns including squarelike pinwheels, (anti)spirals with phase-randomized core...