The biological competition problem

This paper addresses the biological competition stability problem among organisms of the same or different species associated with the need for a common resource that occurs in a limited supply relative to demand by considering it as a discrete event dynamical system. Timed Petri nets are a graphical and mathematical modeling tool applicable to discrete event dynamical systems in order to represent its states evolution. Lyapunov stability theory provides the required tools needed to aboard the stability problem for discrete event dynamical systems modeled with timed Petri nets. By proving boundedness one confirms a dominant oscillating behavior of both organisms dynamics performance. However, the oscillating frequency results to be unknown. This inconvenience is overcome by considering a specific recurrence equation, in the max-plus algebra.