Scale-Free Networks Hidden in Chaotic Dynamical Systems

Details Scale-Free Networks Hidden in Chaotic Dynamical Systems Scale-Free Networks Hidden in Chaotic Dynamical Systems

2010-07-22

arxiv.org/abs/1007.4137v1

Nonlinear Sciences

Chaotic Dynamics

20 pages, 14 figures

Scientific paper

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.

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