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Variational discretization for the planar Lotka–Volterra equations in the Birkhoffian sense

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Abstract

In this paper, we derive the variational characterization of the planar Lotka–Volterra equations in the Birkhoffian sense and ulteriorly construct variational integrators for the group of equations. The planar Lotka–Volterra equations turn out to admit a Birkhoffian representation and consequently can be discretized according to the discrete Birkhoffian equations. By means of the transformation theory of the Birkhoffian equations if necessary, efficient variational integrators of the Lotka–Volterra equations can be obtained. These variational integrators, compared with traditional difference schemes as well as Poisson integrators, have better numerical performance in terms of stability, accuracy and preservation of conserved quantities, demonstrated by numerical results.

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Acknowledgments

The project was supported by the National Natural Science Foundation of China (Grant Nos. 10932002, 10972031 and 11272050), the Scientific Research Foundation, the Excellent Young Teachers Program (Grant No. XN132) and the Construction Plan for Innovative Research Team (Grant No. XN129) of North China University of Technology.

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Authors and Affiliations

  1. College of Science, North China University of Technology, Beijing, 100144, China

    Xinlei Kong

  2. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 100081, China

    Huibin Wu

  3. School of Aerospace Engineering, Beijing Institute of Technology, Beijing, 100081, China

    Fengxiang Mei

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  1. Xinlei Kong
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  2. Huibin Wu
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  3. Fengxiang Mei
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Correspondence to Xinlei Kong.

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Kong, X., Wu, H. & Mei, F. Variational discretization for the planar Lotka–Volterra equations in the Birkhoffian sense. Nonlinear Dyn 84, 733–742 (2016). https://doi.org/10.1007/s11071-015-2522-2

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  • DOI: https://doi.org/10.1007/s11071-015-2522-2

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