The discrete hungry Lotka-Volterra system and a new algorithm for computing matrix eigenvalues

Akiko Fukuda, Emiko Ishiwata, Masashi Iwasaki, Yoshimasa Nakamura

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

The discrete hungry Lotka-Volterra (dhLV) system is a generalization of the discrete Lotka-Volterra (dLV) system which stands for a prey-predator model in mathematical biology. In this paper, we show that (1) some invariants exist which are expressed by dhLV variables and are independent from the discrete time and (2) a dhLV variable converges to some positive constant or zero as the discrete time becomes sufficiently large. Some characteristic polynomial is then factorized with the help of the dhLV system. The asymptotic behaviour of the dhLV system enables us to design an algorithm for computing complex eigenvalues of a certain band matrix.

Original languageEnglish
Article number015007
JournalInverse Problems
Volume25
Issue number1
DOIs
Publication statusPublished - 2009
Externally publishedYes

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Polynomials

ASJC Scopus subject areas

  • Signal Processing
  • Computer Science Applications
  • Applied Mathematics
  • Mathematical Physics
  • Theoretical Computer Science

Cite this

The discrete hungry Lotka-Volterra system and a new algorithm for computing matrix eigenvalues. / Fukuda, Akiko; Ishiwata, Emiko; Iwasaki, Masashi; Nakamura, Yoshimasa.

In: Inverse Problems, Vol. 25, No. 1, 015007, 2009.

Research output: Contribution to journalArticle

Fukuda, Akiko ; Ishiwata, Emiko ; Iwasaki, Masashi ; Nakamura, Yoshimasa. / The discrete hungry Lotka-Volterra system and a new algorithm for computing matrix eigenvalues. In: Inverse Problems. 2009 ; Vol. 25, No. 1.
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