Takaaki Aoki's web page
Mathematical and geographical modelling・Network science・Nonlinear dynamics
数理地理モデリング・ネットワークの数理・非線形動力学
Self-organization of complex networks as a dynamical system
My research interest is self-organization of adaptive networks. Real-world networks are not static, but continuously change to meet the evolving needs of society. To know where the networks will change, we need to understand the nature of changing networks, in which the reformation of the networks and the dynamical processes occurring on the network are interdependent.
To understand the mechanisms governing such dynamical network organization, we proposed a simple model of co-evolving network dynamics taking account of the interplay between them, combining the dynamics of random walkers and the dynamics of the weighted network. We considered a single quantity at each node as the `resource’, which can be regarded as, for example, molecules, cells, people, money, or data packets. We introduced a diffusion dynamics of the resource on a weighted network. Simultaneously, we assumed that the interactions between the nodes change with time as a function of the resource.
Then, we studied how the resource distributes on the network at the equilibrium state, and at the same time, what type of structure of the weighted network is organized. We then found that under suitable conditions, the quantities of the resource and the link weights converge to stationary power-law distributions at the macroscopic level, but they continue to change with time at the microscopic level (See a movie below), even though the dynamics of the proposed model is completely deterministic without any random processes. We numerically and theoretically analyzed the equilibrium states from perspective of the dynamical system and found that the system has multi- stability including chaotic states. For details, please see the following paper.
Literature
-
Scale-Free Structures Emerging from Co-Evolution of a Network and the Distribution of a Diffusive Resource on It, Takaaki AOKI and Toshio AOYAGI,
Physical Review Letters, vol.109, 208702 (2012).
DOI: 10.1103/PhysRevLett.109.208702 -
Self-organization of complex networks as a dynamical system, Takaaki AOKI , Koichiro YAWATA and Toshio AOYAGI,
Physical Review E, vol.91, 012908 (2015).
DOI: 10.1103/PhysRevE.91.012908