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Periodic Solutions for the Degenerate Lotka–Volterra Competition System

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Abstract

In this paper we consider periodic solutions for the degenerate Lotka–Volterra competition system. We use the iteration method and energy method to prove the existence of periodic solutions. Furthermore, we give some numerical simulations and explicit solutions to verify our theoretical results. As far as we know, there are no results about the periodic solutions for degenerate Lotka–Volterra competition system before the present work.

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Acknowledgements

The authors would like to thank the anonymous referees for their valuable comments and suggestions, which made some significant changes in this paper. The research of H. Huang was supported by Guangdong Basic and Applied Basic Research Foundation, No. 2019A1515110074. The research of R. Huang was supported in part by NSFC Grant Nos. 11671155, 11771155 and 11971179, Guangdong Basic and Applied Basic Research Foundation Nos. 2020A1515010338, 2020B1515310005 and 2020B1515310013. The research of L. Wang was supported in part by NSFC Grant Nos. 11771156 and 11371153, NSF of CQ Grant No. cstc2019jcyj-msxmX0381, Chongqing Municipal Key Laboratory of Institutions of Higher Education Grant No. [2017]3 and the research project of Chongqing Three Gorges University Grant No. 17ZP13. The research of J. Yin was supported by NSFC Grant No. 11771156, NSF of Guangdong Grant No. 2020B1515310013, NSF of Guangzhou Grant No. 201804010391 and Natural Science Foundation of Guangdong Province (Grant No. 2017A030313003).

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Authors and Affiliations

  1. School of Mathematics and Big Data, Foshan University, Foshan, 528000, China

    Haochuan Huang

  2. School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, China

    Rui Huang & Jingxue Yin

  3. Key Laboratory for Nonlinear Science and System Structure, College of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing, 404100, China

    Liangwei Wang

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  1. Haochuan Huang
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  2. Rui Huang
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  4. Jingxue Yin
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Correspondence to Rui Huang.

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Huang, H., Huang, R., Wang, L. et al. Periodic Solutions for the Degenerate Lotka–Volterra Competition System. Qual. Theory Dyn. Syst. 19, 73 (2020). https://doi.org/10.1007/s12346-020-00409-x

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