Monotonic convergence to eigenvalues of totally nonnegative matrices in an integrable variant of the discrete lotka-volterra system

Akihiko Tobita, Akiko Fukuda, Emiko Ishiwata, Masashi Iwasaki, Yoshimasa Nakamura

研究成果: Conference contribution

抄録

The Lotka-Volterra (LV) system describes a simple predator-prey model in mathematical biology. The hungry Lotka-Volterra (hLV) system assumed that each predator preys on two or more species is an extension; those involving summations and products of nonlinear terms are referred to as summation-type and product-type hLV systems, respectively. Time-discretizations of these systems are considered in the study of integrable systems, and have been shown to be applicable to computing eigenvalues of totally nonnegative (TN) matrices. Monotonic convergence to eigenvalues of TN matrices, however, has not yet been observed in the time-discretization of the product-type hLV system. In this paper, we show the existence of a center manifold associated with the time-discretization of the product-type hLV system, and then clarify how the solutions approach an equilibrium corresponding to the eigenvalues of TN matrices in the final phase of convergence.

本文言語English
ホスト出版物のタイトルEigenvalue Problems
ホスト出版物のサブタイトルAlgorithms, Software and Applications in Petascale Computing - EPASA 2015
編集者Yoshinobu Kuramashi, Takeo Hoshi, Tetsuya Sakurai, Toshiyuki Imamura, Shao-Liang Zhang, Yusaku Yamamoto
出版社Springer Verlag
ページ157-169
ページ数13
ISBN(印刷版)9783319624242
DOI
出版ステータスPublished - 2017
イベント1st InternationalWorkshop on Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing, EPASA 2015 - Tsukuba, Japan
継続期間: 2015 9 142015 9 16

出版物シリーズ

名前Lecture Notes in Computational Science and Engineering
117
ISSN(印刷版)1439-7358

Other

Other1st InternationalWorkshop on Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing, EPASA 2015
国/地域Japan
CityTsukuba
Period15/9/1415/9/16

ASJC Scopus subject areas

  • モデリングとシミュレーション
  • 工学(全般)
  • 離散数学と組合せ数学
  • 制御と最適化
  • 計算数学

フィンガープリント

「Monotonic convergence to eigenvalues of totally nonnegative matrices in an integrable variant of the discrete lotka-volterra system」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル