title: Self-organization of complex networks as a dynamical system.
abstract: To understand the dynamics of real-world networks, we investigate a mathematical model of the interplay between the dynamics of random walkers on a weighted network and the link weights driven by a resource carried by the walkers. Our numerical studies reveal that, under suitable conditions, the co-evolving dynamics lead to the emergence of stationary power-law distributions of the resource and link weights, while the resource quantity at each node ceaselessly changes with time. We analyze the network organization as a deterministic dynamical system and find that the system exhibits multistability, with numerous fixed points, limit cycles, and chaotic states. The chaotic behavior of the system leads to the continual changes in the microscopic network dynamics in the absence of any external random noises. We conclude that the intrinsic interplay between the states of the nodes and network reformation constitutes a major factor in the vicissitudes of real-world networks.
authors: Faculty of Education, Kagawa University, Takamatsu 760-8521, Japan.
authors: Takaaki
authors: T
authors: Aoki
authors: Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan.
authors: Koichiro
authors: K
authors: Yawata
authors: Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan and CREST, Japan Science and Technology Agency, Kawaguchi, Saitama 332-0012, Japan.
authors: Toshio
authors: T
authors: Aoyagi
mesh_terms: D004058:Diffusion; D017711:Nonlinear Dynamics