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Spatial dynamics of a vegetation model in an arid flat environment

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Abstract

Self-organized vegetation patterns in space were found in arid and semi-arid areas. In this paper, we modelled a vegetation model in an arid flat environment using reaction-diffusion form and investigated the pattern formation. By using Hopf and Turing bifurcation theory, we obtain Turing region in parameters space. It is found that there are different types of stationary patterns including spotted, mixed, and stripe patterns by amplitude equation. Moreover, we discuss the changes of the wavelength with respect to biological parameters. Specifically, the wavelength becomes smaller as rainfall increases and larger as plant morality increases. The results may well explain the vegetation pattern observed in the real world and provide some new insights on preventing from desertification.

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Acknowledgements

The research was partially supported by the National Natural Science Foundation of China under Grant No. 11147015, Natural Science Foundation of Shan’Xi Province Grant Nos. 2012021002-1 and 2012011002-2, the opening foundation of the Institute of Information Economy, Hangzhou Normal University, Grant No. PD12001003002003, International and Technical Cooperation Project of Shanxi Province (2010081005) and Graduate Students’ Excellent Innovative Item of Shanxi Province No. 20113107.

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Authors and Affiliations

  1. Institute of Information Economy, Hangzhou Normal University, Hangzhou, 310036, People’s Republic of China

    Gui-Quan Sun & Zi-Ke Zhang

  2. Department of Mathematics, North University of China, Taiyuan, Shan’xi, 030051, People’s Republic of China

    Gui-Quan Sun

  3. Department of Mathematics, Taiyuan Institute of Technology, Taiyuan, Shan’xi, 030008, People’s Republic of China

    Li Li

  4. Web Sciences Center, University of Electronic Science and Technology of China, Chengdu, Sichuan, 610054, People’s Republic of China

    Zi-Ke Zhang

  5. Department of Physics, University of Fribourg, Chemin du Musée 3, 1700, Fribourg, Switzerland

    Zi-Ke Zhang

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  1. Gui-Quan Sun
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Correspondence to Gui-Quan Sun.

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Sun, GQ., Li, L. & Zhang, ZK. Spatial dynamics of a vegetation model in an arid flat environment. Nonlinear Dyn 73, 2207–2219 (2013). https://doi.org/10.1007/s11071-013-0935-3

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  • DOI: https://doi.org/10.1007/s11071-013-0935-3

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