Dynamics on complex networks and its applications : focused on the synchronization

Abstract

We study the dynamic behaviors of synchronization and random fields Ising models on complex networks, in which the effects of static topological properties to the dynamic behaviors of each model are investigated thoroughly for various network models such as globally connected networks, random networks, small-world networks, and scale-free networks. Especially focused on the synchronization phenomena, we study the relaxation dynamics of synchrony on various complex networks and investigate how the order of synchronization can be controlled by increasing the directionality on directed networks. In order to study general synchronization more, we extend Kuramoto synchronization model to the more general active rotator models. On the studying the dynamics of random fields Ising models on complex networks, we invent a new community finding method adapting the ground states properties of zero-temperature random fields Ising model. Applying our community finding method to various social networks, community structures are successfully revealed as a ground state domains of Ising spins. Furthermore based on the understanding of the static and dynamic properties of complex networks, we apply useful network concepts to the biological data to investigate hidden properties of biological systems. First, we study collective synchronization in a large number of coupled oscillators on various complex networks. In particular, we focus on the relaxation dynamics of synchronization, which is an important issue from the viewpoint of information transfer or the dynamics of system recovery after a perturbation. From this study we find out that the network relaxation time does not depend on the network size but depend on the order of desynchronized states. Furthermore, we investigate how we can improve the order of synchronization just by changing the link direction conserving the local linking cost and topology. We propose the residual degree gradient network method to increase the...