Asymptotic analysis for an extended discrete Lotka-Volterra system related to matrix eigenvalues

You Takahashi, Masashi Iwasaki, Akiko Fukuda, Emiko Ishiwata, Yoshimasa Nakamura

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

The integrable discrete hungry Lotka-Volterra (dhLV) system is easily transformed to the qd-type dhLV system, which resembles the recursion formula of the qd algorithm for computing matrix eigenvalues. Some of the qd-type dhLV variables play a role for assisting the time evolution of the others. This property does not appear in the original dhLV system. In this article, we first show the existence of a centre manifold for the qd-type dhLV system. With the help of the centre manifold theory, we next investigate the local convergence of the qd-type dhLV system, and then clarify the monotonicity related to the qd-type dhLV variables at the final phase of the convergence.

Original languageEnglish
Pages (from-to)586-594
Number of pages9
JournalApplicable Analysis
Volume92
Issue number3
DOIs
Publication statusPublished - 2013 Mar 1
Externally publishedYes

Keywords

  • asymptotic behaviour
  • centre manifold theory
  • the discrete hungry Lotka-Volterra system

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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