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

Abstract

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. Keywordspredator-prey systems, stability of the systems, Lyapunov method, max-plus algebra, timed petri net AbstrakDalam paper ini, dibahas pengertian aljabar max-plus dan sifat-sifatnya. Selanjutnya dengan menggunakan Petri net berwaktu dikonstruksi suatu model sistem mangsa-pemangsa dan dianalisa kestabilan serta perilaku periodik sistem. Dengan menggunakan kestabilan Lyapunov diperoleh syarat cukup masalah kestabilan dan durasi osilasi dapat ditentukan. Kata kuncisistem mangsa-pemangsa, kestabilan sistem, kestabilan Lyapunov, aljabar max-plus, petri net berwaktu