TY - JOUR
T1 - On some properties of a discrete hungry Lotka-Volterra system of multiplicative type
AU - Hama, Yosuke
AU - Fukuda, Akiko
AU - Yamamoto, Yusaku
AU - Iwasaki, Masashi
AU - Ishiwata, Emiko
AU - Nakamura, Yoshimasa
PY - 2012
Y1 - 2012
N2 - Two kinds of discrete hungry Lotka-Volterra systems (dhLV) are known as discretizations of the additive type hungry Lotka-Volterra system and the multiplicative one. By associating the dhLV of additive type (dhLVI) and the discrete hungry Toda equation (dhToda) with LR transformations, some of the authors give a Bäcklund transformation between these two systems. In this paper, from the dhLV of multiplicative type (dhLVII), we first derive the qd-type dhLVII. Through finding the positivity of the qd-type dhLVII and the LR transformation associated with the dhLVII, we present Bäcklund transformations among the dhLVI, the dhLVII and the dhToda. Moreover, by using one of the Bäcklund transformations, we show asymptotic convergence of the qd-type dhLVII.
AB - Two kinds of discrete hungry Lotka-Volterra systems (dhLV) are known as discretizations of the additive type hungry Lotka-Volterra system and the multiplicative one. By associating the dhLV of additive type (dhLVI) and the discrete hungry Toda equation (dhToda) with LR transformations, some of the authors give a Bäcklund transformation between these two systems. In this paper, from the dhLV of multiplicative type (dhLVII), we first derive the qd-type dhLVII. Through finding the positivity of the qd-type dhLVII and the LR transformation associated with the dhLVII, we present Bäcklund transformations among the dhLVI, the dhLVII and the dhToda. Moreover, by using one of the Bäcklund transformations, we show asymptotic convergence of the qd-type dhLVII.
M3 - Article
VL - 4A
SP - 5
EP - 15
JO - Journal of Math-for-Industry
JF - Journal of Math-for-Industry
ER -