Reversible boolean networks II: Phase transition, oscillation, and local structures

Details Reversible boolean networks II: Phase transition, oscillation, and local structures Reversible boolean networks II: Phase transition, oscillation, and local structures

2000-09-01

arxiv.org/abs/cond-mat/0009019v2

Physics

Condensed Matter

Disordered Systems and Neural Networks

31 pages, 15 figures, 2 tables

Scientific paper

10.1016/S0167-2789(01)00286-X

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 $K_c\approx 1.65$ 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

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