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The Biological Interaction Stability Problem

  • Zvi Retchkiman Konigsberg
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7331)

Abstract

This paper addresses the biological interaction 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.

Keywords

Biological interaction Discrete Event Dynamical Systems Max-Plus Algebra Lyapunov Method Timed Petri Nets 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Zvi Retchkiman Konigsberg
    • 1
  1. 1.Instituto Politecnico NacionalMexico

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