An asymptotic analysis for an integrable variant of the Lotka-Volterra prey--predator model via a determinant expansion technique
An asymptotic analysis for an integrable variant of the Lotka-Volterra prey--predator model via a determinant expansion technique
复制标题
通过行列式展开技术对 Lotka-Volterra 猎物-捕食者模型的可积变体进行渐近分析
DOI：
10.1080/23311835.2015.1046538
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发表时间：
2015
影响因子：
--
通讯作者：
Yusaku Yamamoto and Yoshimasa Nakamura
中科院分区：
文献类型：
--
作者：
Masato Shinjo;Masashi Iwasaki;Akiko Fukuda;Emiko Ishiwata;Yusaku Yamamoto and Yoshimasa Nakamura
汉克尔行列式出现在若干可积系统解的表示中。因此，汉克尔行列式的渐近展开式在研究这类可积系统的渐近分析中起着关键作用。本文给出了一类Casorati行列式的渐近展开式，作为Hankel情形的推广。这个Casorati行列式随后被证明与离散饥饿Lotka-Volterra （dhLV）系统的解有关，该系统是数学生物学中著名的猎物-捕食者模型的可积变体。最后，利用Casorati行列式的展开式阐明了dhLV系统的渐近性质。
The Hankel determinant appears in representations of solutions to several integrable systems. An asymptotic expansion of the Hankel determinant thus plays a key role in the investigation of asymptotic analysis of such integrable systems. This paper presents an asymptotic expansion formula of a certain Casorati determinant as an extension of the Hankel case. This Casorati determinant is then shown to be associated with the solution to the discrete hungry Lotka–Volterra (dhLV) system, which is an integrable variant of the famous prey–predator model in mathematical biology. Finally, the asymptotic behavior of the dhLV system is clarified using the expansion formula for the Casorati determinant.