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 → …

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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