Transient problem for Boolean Monomial Dynamical Systems : Towards a solution of the transient problem for boolean monomial dynamical systems

ISBN-13: 9786139062539 / Angielski / Miękka / 2018 / 56 str.

Xavier Antonio Terán Batista

Opis

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.

O autorze

Terán Batista, Xavier Antonio
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.