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Reversible Boolean Networks I: Distribution of Cycle Lengths by Coppersmith, S. N.; Kadanoff, Leo P.; Zhang, Zhitong is a scholarly article available to read on EtoBox.

What is Reversible Boolean Networks I: Distribution of Cycle Lengths about?

We consider a class of models describing the dynamics of $N$ Boolean variables, where the time evolution of each depends on the values of $K$ of the other variables. Previous work has considered models with dissipative dynamics. Here we consider time-reversible models, which necessarily have the property that every possible point in the state-space is an element of one and only one cycle. As in the dissipative case, when K is large, typical orbit lengths grow exponentially with N, whereas for small enough K, typical orbit lengths grow much more slowly with N. The numerical data are consistent with the existence of a phase transition at which the average orbit length grows as a power of N at a value of K between 1.4 and 1.7. However, in the reversible models the interplay between the discrete symmetry and quenched randomness can lead to enormous fluctuations of orbit lengths and other interesting features that are unique to the reversible case. The orbits can be classified by their behavior under time reversal. The orbits that transform into themselves under time reversal have properties quite different from those that do not; in particular, a significant fraction of latter-type orb

Author

Coppersmith, S. N.; Kadanoff, Leo P.; Zhang, Zhitong

Published

2000

Language

EN