TY - GEN
T1 - The biological interaction stability problem
AU - Retchkiman Konigsberg, Zvi
PY - 2012
Y1 - 2012
N2 - 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.
AB - 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.
KW - Biological interaction
KW - Discrete Event Dynamical Systems
KW - Lyapunov Method
KW - Max-Plus Algebra
KW - Timed Petri Nets
UR - http://www.scopus.com/inward/record.url?scp=84875121664&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-30976-2_1
DO - 10.1007/978-3-642-30976-2_1
M3 - Contribución a la conferencia
SN - 9783642309755
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 1
EP - 10
BT - Advances in Swarm Intelligence - Third International Conference, ICSI 2012, Proceedings
T2 - 3rd International Conference on Swarm Intelligence, ICSI 2012
Y2 - 17 June 2012 through 20 June 2012
ER -