植被系统, Hopf 分支, Turing 分支 , Turing--Hopf 分支

Vegetation pattern is one of the typical characteristics of ecosystems in arid and semi­arid areas, which can qualitatively describe the spatial distribution structure of vegetation, and can be used as an early indicator of ecosystem improvement and degradation. This paper devotes to summarize the bifurcation phenomena in vegetation system to reveal the formation mechanism of vegetation pattern and provide warning signals of desertification. Firstly, through the Hopf bifurcation theory, the conditions of spatial homogeneous Hopf bifurcation in vegetation model are qualitatively analyzed, and the phenomenon of interannual periodic fluctuation of vegetation biomass is explained. Secondly, the existing vegetation models are analyzed by the Turing bifurcation theory, the regular distribution of

vegetation in space and the formation mechanism of pattern are revealed, and the types of these patterns are refined by applying the multiple scale analysis method, and the parameter threshold of the system undergoing pattern phase transition is found. Finally, when the Hopf bifurcation and Turing bifurcation occur at the same time, the system will undergo a Turing-­Hopf bifurcation. By means of the normal form theory of reaction­diffusion equation, the normal form of the Turing­-Hopf bifurcation is derived, and the amplitude equation is obtained by the cylindrical coordinate  transformation to analyze its dynamic behavior, and then more complex spatiotemporal patterns of vegetation are revealed.

Vegetation system, Hopf bifurcation, Turing bifurcation, Turing--Hopf bifurcation