Nonlinear Dynamics

, Volume 73, Issue 4, pp 2207–2219

Spatial dynamics of a vegetation model in an arid flat environment

Original Paper

DOI: 10.1007/s11071-013-0935-3

Cite this article as:
Sun, G., Li, L. & Zhang, Z. Nonlinear Dyn (2013) 73: 2207. doi:10.1007/s11071-013-0935-3


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.


Vegetation modelBifurcationPatternWavelengthDesertification

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Institute of Information EconomyHangzhou Normal UniversityHangzhouPeople’s Republic of China
  2. 2.Department of MathematicsNorth University of ChinaTaiyuanPeople’s Republic of China
  3. 3.Department of MathematicsTaiyuan Institute of TechnologyTaiyuanPeople’s Republic of China
  4. 4.Web Sciences CenterUniversity of Electronic Science and Technology of ChinaChengduPeople’s Republic of China
  5. 5.Department of PhysicsUniversity of FribourgFribourgSwitzerland