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• W4299535097 abstract "We continue our consideration of a class of models describing the reversible dynamics of $N$ Boolean variables, each with $K$ inputs. We investigate in detail the behavior of the Hamming distance as well as of the distribution of orbit lengths as $N$ and $K$ are varied. We present numerical evidence for a phase transition in the behavior of the Hamming distance at a critical value $K_capprox 1.65$ and also an analytic theory that yields the exact bounds on $1.5 le K_c le 2.$ We also discuss the large oscillations that we observe in the Hamming distance for $K<K_c$ as a function of time as well as in the distribution of cycle lengths as a function of cycle length for moderate $K$ both greater than and less than $K_c$. We propose that local structures, or subsets of spins whose dynamics are not fully coupled to the other spins in the system, play a crucial role in generating these oscillations. The simplest of these structures are linear chains, called linkages, and rings, called circuits. We discuss the properties of the linkages in some detail, and sketch the properties of circuits. We argue that the observed oscillation phenomena can be largely understood in terms of these local structures." @default.
• W4299535097 created "2022-10-02" @default.
• W4299535097 creator A5047710475 @default.
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• W4299535097 date "2001-09-01" @default.
• W4299535097 modified "2023-10-14" @default.
• W4299535097 title "Reversible Boolean networks" @default.
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• W4299535097 doi "https://doi.org/10.1016/s0167-2789(01)00286-x" @default.
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