Journal
NONLINEAR DYNAMICS
Volume 73, Issue 4, Pages 2207-2219Publisher
SPRINGER
DOI: 10.1007/s11071-013-0935-3
Keywords
Vegetation model; Bifurcation; Pattern; Wavelength; Desertification
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Funding
- National Natural Science Foundation of China [11147015]
- Natural Science Foundation of Shan'Xi Province [2012021002-1, 2012011002-2]
- opening foundation of the Institute of Information Economy, Hangzhou Normal University [PD12001003002003]
- International and Technical Cooperation Project of Shanxi Province [2010081005]
- Graduate Students' Excellent Innovative Item of Shanxi Province [20113107]
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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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