Volume 33, Issue 5
Integrable Discretisation of the Lotka-Volterra System

Yang He ,  Yajuan Sun and Zaijiu Shang

10.4208/jcm.1504-m4543

J. Comp. Math., 33 (2015), pp. 468-494.

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  • Abstract

In this paper, we apply Hirota'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 volumepreserving 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.

  • History

Published online: 2015-10

  • AMS Subject Headings

65L12, 65P99, 37M05.

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