  In this paper, we show our discovery that state-transition networks in
several chaotic dynamical systems are "scale-free networks," with a technique
to understand a dynamical system as a whole, which we call the analysis for
"Discretized-State Transition" (DST) networks; This scale-free nature is found
universally in the logistic map, the sine map, the cubic map, the general
symmetric map, the sine-circle map, the Gaussian map, and the delayed logistic
map. Our findings prove that there is a hidden order in chaos, which has not
detected yet. Furthermore, we anticipate that our study opens up a new way to a
"network analysis approach to dynamical systems" for understanding complex
phenomena.
