Ocasio, Víctor A.

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Stability of boolean dynamical systems and graph periodicity
(2009-05) Ocasio, Víctor A.; Colón-Reyes, Omar; College of Arts and Sciences - Sciences; Bollman, Dorothy; Castellini, Gabriele; Department of Mathematics; Macchiavelli, Raúl E.
In the study of finite dynamical systems it is important to develop efficient algorithms that provide information about the dynamics of the systems. Criteria for determining when a system described by monomials, over the two element field, is a fixed point, have already been determined. We make use of such criteria to study the concept of stability for finite dynamical systems. In order to do this, we use the fact that a monomial dynamical system’s cycle structure can be described by the structure of the monomials. This monomial structure can be represented by a digraph. The algorithms presented in this paper, one for stability, the other for fixed points, combine such criteria with the efficiency of depth-first search rendering both algorithms with complexity O(n 2 log(n)).