Lyapunov-Max-Plus-Algebra Stability in Predator-prey Systems Modeled with Timed Petri Net

In this paper, we discuss the notion of max-plus algebra and their properties. We also construct a model of predator-prey systems with timed Petri net and analyze the stabilization of the systems. Furthermore, we analyze the periodic behavior of the systems. Using the Lyapunov stability theory, we will obtain the sufficient condition for the stabilization problem and the periodic duration of the oscillation will be also determined.