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

doi:10.1007/978-3-319-62426-6_11

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	https://doi.org/10.1007/978-3-319-62426-6_11
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月 14 → 2015 9月 16

出版物シリーズ

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

Other

Other	1st InternationalWorkshop on Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing, EPASA 2015
国/地域	Japan
City	Tsukuba
Period	15/9/14 → 15/9/16

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

文献へのアクセス

10.1007/978-3-319-62426-6_11

他のファイルとリンク

フィンガープリント

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引用スタイル

Tobita, A., Fukuda, A., Ishiwata, E., Iwasaki, M., & Nakamura, Y. (2017). Monotonic convergence to eigenvalues of totally nonnegative matrices in an integrable variant of the discrete lotka-volterra system. In Y. Kuramashi, T. Hoshi, T. Sakurai, T. Imamura, S-L. Zhang, & Y. Yamamoto (Eds.), Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing - EPASA 2015 (pp. 157-169). (Lecture Notes in Computational Science and Engineering; Vol. 117). Springer Verlag. https://doi.org/10.1007/978-3-319-62426-6_11

Monotonic convergence to eigenvalues of totally nonnegative matrices in an integrable variant of the discrete lotka-volterra system. / Tobita, Akihiko; Fukuda, Akiko; Ishiwata, Emiko その他.

Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing - EPASA 2015. ed. / Yoshinobu Kuramashi; Takeo Hoshi; Tetsuya Sakurai; Toshiyuki Imamura; Shao-Liang Zhang; Yusaku Yamamoto. Springer Verlag, 2017. p. 157-169 (Lecture Notes in Computational Science and Engineering; Vol. 117).

研究成果: Conference contribution

Tobita, A, Fukuda, A, Ishiwata, E, Iwasaki, M & Nakamura, Y 2017, Monotonic convergence to eigenvalues of totally nonnegative matrices in an integrable variant of the discrete lotka-volterra system. in Y Kuramashi, T Hoshi, T Sakurai, T Imamura, S-L Zhang & Y Yamamoto (eds), Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing - EPASA 2015. Lecture Notes in Computational Science and Engineering, vol. 117, Springer Verlag, pp. 157-169, 1st InternationalWorkshop on Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing, EPASA 2015, Tsukuba, Japan, 15/9/14. https://doi.org/10.1007/978-3-319-62426-6_11

Tobita A, Fukuda A, Ishiwata E, Iwasaki M, Nakamura Y. Monotonic convergence to eigenvalues of totally nonnegative matrices in an integrable variant of the discrete lotka-volterra system. In Kuramashi Y, Hoshi T, Sakurai T, Imamura T, Zhang S-L, Yamamoto Y, editors, Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing - EPASA 2015. Springer Verlag. 2017. p. 157-169. (Lecture Notes in Computational Science and Engineering). doi: 10.1007/978-3-319-62426-6_11

Tobita, Akihiko ; Fukuda, Akiko ; Ishiwata, Emiko その他. / Monotonic convergence to eigenvalues of totally nonnegative matrices in an integrable variant of the discrete lotka-volterra system. Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing - EPASA 2015. editor / Yoshinobu Kuramashi ; Takeo Hoshi ; Tetsuya Sakurai ; Toshiyuki Imamura ; Shao-Liang Zhang ; Yusaku Yamamoto. Springer Verlag, 2017. pp. 157-169 (Lecture Notes in Computational Science and Engineering).

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