Asymptotic analysis for an extended discrete LotkaVolterra system related to matrix eigenvalues

作者：Takahashi You; Iwasaki Masashi^*; Fukuda Akiko; Ishiwata Emiko; Nakamura Yoshimasa

来源：Applicable Analysis, 2013, 92(3): 586-594.

DOI：10.1080/00036811.2011.631915

• the discrete hungry Lotka-Volterra system
• centre manifold theory
• asymptotic behaviour

The integrable discrete hungry LotkaVolterra (dhLV) system is easily transformed to the qd-type dhLV system, which resembles the recursion formula of the qd algorithm for computing matrix eigenvalues. Some of the qd-type dhLV variables play a role for assisting the time evolution of the others. This property does not appear in the original dhLV system. In this article, we first show the existence of a centre manifold for the qd-type dhLV system. With the help of the centre manifold theory, we next investigate the local convergence of the qd-type dhLV system, and then clarify the monotonicity related to the qd-type dhLV variables at the final phase of the convergence.

• 出版日期2013-3-1