The biological interaction stability problem

Zvi Retchkiman Konigsberg

doi:10.1007/978-3-642-30976-2_1

The biological interaction stability problem

Zvi Retchkiman Konigsberg

Centro de Investigación en Computación (CIC)

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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.

Original language	English
Title of host publication	Advances in Swarm Intelligence - Third International Conference, ICSI 2012, Proceedings
Pages	1-10
Number of pages	10
Edition	PART 1
DOIs	https://doi.org/10.1007/978-3-642-30976-2_1
State	Published - 2012
Event	3rd International Conference on Swarm Intelligence, ICSI 2012 - Shenzhen, China Duration: 17 Jun 2012 → 20 Jun 2012

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Number	PART 1
Volume	7331 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	3rd International Conference on Swarm Intelligence, ICSI 2012
Country/Territory	China
City	Shenzhen
Period	17/06/12 → 20/06/12

Keywords

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

Access to Document

10.1007/978-3-642-30976-2_1

Cite this

Retchkiman Konigsberg, Z. (2012). The biological interaction stability problem. In Advances in Swarm Intelligence - Third International Conference, ICSI 2012, Proceedings (PART 1 ed., pp. 1-10). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7331 LNCS, No. PART 1). https://doi.org/10.1007/978-3-642-30976-2_1

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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.",

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Retchkiman Konigsberg, Z 2012, The biological interaction stability problem. in Advances in Swarm Intelligence - Third International Conference, ICSI 2012, Proceedings. PART 1 edn, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), no. PART 1, vol. 7331 LNCS, pp. 1-10, 3rd International Conference on Swarm Intelligence, ICSI 2012, Shenzhen, China, 17/06/12. https://doi.org/10.1007/978-3-642-30976-2_1

The biological interaction stability problem. / Retchkiman Konigsberg, Zvi.
Advances in Swarm Intelligence - Third International Conference, ICSI 2012, Proceedings. PART 1. ed. 2012. p. 1-10 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7331 LNCS, No. PART 1).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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The biological interaction stability problem

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