Emergence of fit-get-rich networks from chaotic attractors

Connecting dynamical information of the nonlinear dynamical systems to the temporal evolution of complex networks, we analyze nonlinear dynamical systems with complex-network theory. We dynamically construct networks from attractors of nonlinear dynamical systems depending on their dynamical information and thereby we can evaluate the attractors through the evolution processes of constructed networks. As a result, we find that the constructed networks from periodic attractors correspond to the first-mover-advantage phase and those from chaotic attractors correspond to the fit-get-rich phase. We also show that the fit-get-rich property is originated to an essential mechanism for producing chaotic dynamics—stretching and folding.