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 vol...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 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.展开更多
基金The authors would like to thank J. Niesen for his helpful suggestions in improving the presentation of the paper. The first author was supported by the Fundamental Research Funds for the Central Universities （WK2030040057）. The second author was sup- ported by the National Natural Science Foundation of China （11271357）, the Foundation for Innovative Research Groups of the NNSFC （11321061） and the ITER-China Program （2014G- B124005）. The third author was supported by the Foundation of the NNSFC （10990012） and the Marine Public Welfare Project of China （201105032）.
文摘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 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.
