Stability Problem for a Predator-Prey System
This paper considers the growth rate dynamics of a predator-prey system as a discrete event dynamical system. Timed Petri nets are a graphical and mathematical modeling tool applicable to discrete event systems in order to represent its states evolution. Lyapunov stability theory provides the required tools needed to aboard the stability problem for the predator-prey system treated as a discrete event system modeled with timed petri nets. By proving boundedness one confirms a dominant oscillating behavior of both populations 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.
KeywordsPredator-Prey System Discrete Event Dynamical Systems Max-Plus Algebra Lyapunov Method Timed Petri Nets
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