Open AccessTime-delay version of the integrable discrete Lotka-Volterra system in terms of the LR transformations
Author(s) -
Masaki Sekiguchi,
Kurumi Oka,
Masashi Iwasaki,
Emiko Ishiwata
Publication year - 2021
Publication title -
iop scinotes
Language(s) - English
Resource type - Journals
ISSN - 2633-1357
DOI - 10.1088/2633-1357/ac1cd4
Subject(s) - integrable system , eigenvalues and eigenvectors , mathematics , discretization , discrete time and continuous time , convergence (economics) , matrix (chemical analysis) , mathematical optimization , mathematical analysis , statistics , physics , materials science , quantum mechanics , economics , composite material , economic growth
To introduce time delay into integrable discrete systems, we present a time-delay version of the discrete Lotka-Volterra (dLV) system, which is a time-discretization of the famous predator-prey Lotka-Volterra system. Focusing on the LR transformations, which has been designed for solving symmetric eigenvalue problems, plays a key role in deriving the essential properties of the original dLV system. We also clarify asymptotic convergence in the resulting time-delay system and present an application for computing matrix eigenvalues and singular values.