For critical K=1 Boolean networks, attractor lengths are governed by the order of the permutation induced by feedback loops, yielding typical maximum lengths exp[(1/2)ln^2 N], extremal lengths exp[sqrt(N ln N)], and mean length exp[N^(1/3)].
Insights from number theory into the critical kauffman model with connectivity one.Journal of Physics A: Mathematical and Theoretical, 57(27):275003, 2024
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Permutation theory governs long-term dynamics of critical Boolean networks
For critical K=1 Boolean networks, attractor lengths are governed by the order of the permutation induced by feedback loops, yielding typical maximum lengths exp[(1/2)ln^2 N], extremal lengths exp[sqrt(N ln N)], and mean length exp[N^(1/3)].