@Article{JCM-33-468,
author = {He , YangSun , Yajuan and Shang , Zaijiu},
title = {Integrable Discretisation of the Lotka-Volterra System},
journal = {Journal of Computational Mathematics},
year = {2015},
volume = {33},
number = {5},
pages = {468--494},
abstract = {<p style="text-align: justify;">In this paper, we apply Hirota&#39;s discretisation to a three-dimensional integrable Lotka-Volterra system. By analyzing the three-dimensional modified equation of the resulting numerical method, we show that it is volume-preserving, and has two independent first integrals. Moreover, it can be formally reduced to a system in one dimension via a volume-preserving transformation. If the given initial value is located in the positive octant, we prove that the numerical solution is confined to a one-dimensional connected and compact space which is diffeomorphic to a circle.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.1504-m4543},
url = {http://global-sci.org/intro/article_detail/jcm/9855.html}
}