TY - JOUR

T1 - The biological competition problem

AU - Retchkiman Konigsberg, Zvi

PY - 2012/6/1

Y1 - 2012/6/1

N2 - This paper addresses the biological competition 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. © Dynamic Publishers, Inc.

AB - This paper addresses the biological competition 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. © Dynamic Publishers, Inc.

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M3 - Article

SP - 215

EP - 226

JO - Neural, Parallel and Scientific Computations

JF - Neural, Parallel and Scientific Computations

SN - 1061-5369

ER -