Network organization as a dynamical system*

Real-world networks are not static, but continuously change to meet the evolving needs of society. To manage and control such dynamic networks, we studied a simple model of co-evolving network dynamics, combining the dynamics of random walkers and the dynamics of weighted connections that are regulated by the traffic of the walkers. Under suitable conditions, the density of the walkers and the link weights converged to stationary power-law distributions at the macroscopic level. However, they continued to change with time at the microscopic level, even though the dynamics of the proposed model is completely deterministic. We numerically analyzed the equilibrium states from perspective of the dynamical system and found that the system has multi-stability including chaotic states.