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Spatial dynamics of a vegetation model in an arid flat environment |
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| Authors: | Gui-Quan Sun Li Li Zi-Ke Zhang |
| Institution: | 1. Institute of Information Economy, Hangzhou Normal University, Hangzhou, 310036, People’s Republic of China 2. Department of Mathematics, North University of China, Taiyuan, Shan’xi, 030051, People’s Republic of China 3. Department of Mathematics, Taiyuan Institute of Technology, Taiyuan, Shan’xi, 030008, People’s Republic of China 4. Web Sciences Center, University of Electronic Science and Technology of China, Chengdu, Sichuan, 610054, People’s Republic of China 5. Department of Physics, University of Fribourg, Chemin du Musée 3, 1700, Fribourg, Switzerland |
| 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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