Power-law Distributions in the Kauffman Net
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Kauffman net is a dynamical system of logical variables receiving two random inputs and each randomly assigned a boolean function. We show that the attractor and transient lengths exhibit scaleless behavior with power-law distributions over up to ten orders of magnitude. Our results provide evidence for the existence of the "edge of chaos" as a distinct phase between the ordered and chaotic regimes analogous to a critical point in statistical mechanics. The power-law distributions are robust to the changes in the composition of the transition rules and network dynamics.
14 pages, LaTeX, 4 Postscript figures available upon request
14 pages, LaTeX, 4 Postscript figures available upon request