The discrete hungry Lotka–Volterra system and a new algorithm for computing matrix eigenvalues
The discrete hungry Lotka–Volterra system and a new algorithm for computing matrix eigenvalues
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DOI：
10.1088/0266-5611/25/1/015007
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发表时间：
2008
期刊：
影响因子：
2.1
通讯作者：
A. Fukuda;E. Ishiwata;M. Iwasaki;Yoshimasa Nakamura
中科院分区：
文献类型：
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作者：
A. Fukuda;E. Ishiwata;M. Iwasaki;Yoshimasa Nakamura
离散饥饿Lotka-Volterra（dhLV）系统是离散Lotka-Volterra（dLV）系统的推广。本文证明了：（1）存在一些与离散时间无关的dhLV变量;（2）当离散时间足够大时，dhLV变量收敛于某个正常数或零.一些特征多项式，然后因式分解的帮助下的dhLV系统。dhLV系统的渐近行为使我们能够设计一种算法，用于计算某个带矩阵的复特征值。
The discrete hungry Lotka–Volterra (dhLV) system is a generalization of the discrete Lotka–Volterra (dLV) system which stands for a prey–predator model in mathematical biology. In this paper, we show that (1) some invariants exist which are expressed by dhLV variables and are independent from the discrete time and (2) a dhLV variable converges to some positive constant or zero as the discrete time becomes sufficiently large. Some characteristic polynomial is then factorized with the help of the dhLV system. The asymptotic behaviour of the dhLV system enables us to design an algorithm for computing complex eigenvalues of a certain band matrix.