### 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 language | English |
---|---|

Article number | 015007 |

Journal | Inverse Problems |

Volume | 25 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2009 |

Externally published | Yes |

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### ASJC Scopus subject areas

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

### Cite this

*Inverse Problems*,

*25*(1), [015007]. https://doi.org/10.1088/0266-5611/25/1/015007

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

Research output: Contribution to journal › Article

*Inverse Problems*, vol. 25, no. 1, 015007. https://doi.org/10.1088/0266-5611/25/1/015007

}

TY - JOUR

T1 - The discrete hungry Lotka-Volterra system and a new algorithm for computing matrix eigenvalues

AU - Fukuda, Akiko

AU - Ishiwata, Emiko

AU - Iwasaki, Masashi

AU - Nakamura, Yoshimasa

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=62649084069&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=62649084069&partnerID=8YFLogxK

U2 - 10.1088/0266-5611/25/1/015007

DO - 10.1088/0266-5611/25/1/015007

M3 - Article

AN - SCOPUS:62649084069

VL - 25

JO - Inverse Problems

JF - Inverse Problems

SN - 0266-5611

IS - 1

M1 - 015007

ER -