Estabilidad de sistemas dinámicos monomiales sobre cuerpos finitos

Abstract

In 2005, Colón and others [3] gave necessary and sufficient conditions for a monomial dynamical system over a finite field to be a fixed point system, that is, all cycles are of length one. Moreover, in 2009, Ocasio, Colón and others [8] gave necessary and sufficient stabilization conditions for a boolean monomial dynamical system. We make use of such criteria to study the concept of stability over n-tuple cartesian product of the field Fq, where n = 2 and q = 2r +1 prime with r ≥ 1. This work contains necessary and sufficient conditions to determine when a monomial dynamic control system with a unique control variable over [ ] is stabilizable.