Ultradiscrete Lotka-Volterra system computes tropical eigenvalue of symmetric tridiagonal matrices

Akiko Fukuda, Sennosuke Watanabe, Ayumi Hanaoka, Masashi Iwasaki

Research output: Contribution to journalConference article

Abstract

Some of authors' recent study shows that the time evolution of the integrable ultradiscrete Toda equation computes eigenvalue of tridiagonal matrices over min-plus algebra, where min-plus algebra is a semiring with two binary operations: ⊕ : = min and ⊗ : = +. In this paper, we rst present a Backlund transformation between the ultradiscrete Toda equation and the ultradiscrete Lotka-Volterra system. Using the Backlund transformation, we show that the ultradiscrete Lotka-Volterra system can also compute eigenvalue of symmetric tridiagonal matrices over min-plus algebra.

Original languageEnglish
Article number012015
JournalJournal of Physics: Conference Series
Volume1218
Issue number1
DOIs
Publication statusPublished - 2019 May 31
Event3rd International Conference on Mathematics; Pure, Applied and Computation, ICoMPAC 2018 - Surabaya, Indonesia
Duration: 2018 Oct 20 → …

Fingerprint

algebra
eigenvalues
matrices

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Ultradiscrete Lotka-Volterra system computes tropical eigenvalue of symmetric tridiagonal matrices. / Fukuda, Akiko; Watanabe, Sennosuke; Hanaoka, Ayumi; Iwasaki, Masashi.

In: Journal of Physics: Conference Series, Vol. 1218, No. 1, 012015, 31.05.2019.

Research output: Contribution to journalConference article

@article{8207e67dc81843aa8da459f88a636ce2,
title = "Ultradiscrete Lotka-Volterra system computes tropical eigenvalue of symmetric tridiagonal matrices",
abstract = "Some of authors' recent study shows that the time evolution of the integrable ultradiscrete Toda equation computes eigenvalue of tridiagonal matrices over min-plus algebra, where min-plus algebra is a semiring with two binary operations: ⊕ : = min and ⊗ : = +. In this paper, we rst present a Backlund transformation between the ultradiscrete Toda equation and the ultradiscrete Lotka-Volterra system. Using the Backlund transformation, we show that the ultradiscrete Lotka-Volterra system can also compute eigenvalue of symmetric tridiagonal matrices over min-plus algebra.",
author = "Akiko Fukuda and Sennosuke Watanabe and Ayumi Hanaoka and Masashi Iwasaki",
year = "2019",
month = "5",
day = "31",
doi = "10.1088/1742-6596/1218/1/012015",
language = "English",
volume = "1218",
journal = "Journal of Physics: Conference Series",
issn = "1742-6588",
publisher = "IOP Publishing Ltd.",
number = "1",

}

TY - JOUR

T1 - Ultradiscrete Lotka-Volterra system computes tropical eigenvalue of symmetric tridiagonal matrices

AU - Fukuda, Akiko

AU - Watanabe, Sennosuke

AU - Hanaoka, Ayumi

AU - Iwasaki, Masashi

PY - 2019/5/31

Y1 - 2019/5/31

N2 - Some of authors' recent study shows that the time evolution of the integrable ultradiscrete Toda equation computes eigenvalue of tridiagonal matrices over min-plus algebra, where min-plus algebra is a semiring with two binary operations: ⊕ : = min and ⊗ : = +. In this paper, we rst present a Backlund transformation between the ultradiscrete Toda equation and the ultradiscrete Lotka-Volterra system. Using the Backlund transformation, we show that the ultradiscrete Lotka-Volterra system can also compute eigenvalue of symmetric tridiagonal matrices over min-plus algebra.

AB - Some of authors' recent study shows that the time evolution of the integrable ultradiscrete Toda equation computes eigenvalue of tridiagonal matrices over min-plus algebra, where min-plus algebra is a semiring with two binary operations: ⊕ : = min and ⊗ : = +. In this paper, we rst present a Backlund transformation between the ultradiscrete Toda equation and the ultradiscrete Lotka-Volterra system. Using the Backlund transformation, we show that the ultradiscrete Lotka-Volterra system can also compute eigenvalue of symmetric tridiagonal matrices over min-plus algebra.

UR - http://www.scopus.com/inward/record.url?scp=85067798328&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85067798328&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/1218/1/012015

DO - 10.1088/1742-6596/1218/1/012015

M3 - Conference article

AN - SCOPUS:85067798328

VL - 1218

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

SN - 1742-6588

IS - 1

M1 - 012015

ER -