Beschreibung
A problem of interest in finite dynamical systems is to determine when such a system reaches equilibrium, i.e., under what conditions is it a fixed point system. Moreover, given a fixed point system, how many time steps are required to reach a fixed point, i.e., what is its transient? Dorothy Bollman and Omar Colón have shown that a Boolean Monomial Dynamical System (BMDS) f is a fixed point system if and only if every strongly connected component of the dependency graph G_f of f is primitive and in fact, when G_f is strongly connected, the transient of f is equal to the exponent of G_f. Furthermore, every directed graph gives rise to a unique BMDS and hence every example of a primitive graph with known exponent gives us an example of a fixed point BMDS with known transient. Unfortunately, the general problem of determining the exponent of a primitive graph is unsolved. In this work we give several families of primitive graphs for which we can determine the exponent and hence the transient of the corresponding BMDS.
Autorenporträt
Magíster en Ciencias en Matemáticas Pura de la Universidad de Puerto Rico, Recinto de Mayagüez y pregrado como Matemático Puro de la Universidad de Cartagena, poseo formación profesional integral, con principios éticos y valores, capaz de dar soluciones a todo tipo de problemas planteados en el manejo y manipulación de la información.
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