植被系统的时空动力学研究进展  

Progress in Spatiotemporal Dynamics of Vegetation Systems

作　　者：张红桃 孙桂全 Zhang Hongtao;Sun Guiquan(Complex Systems Research Center,Shanxi University,Taiyuan 030006,China;Department of Mathematics,North University of China,Taiyuan 030051,China)

机构地区：[1]山西大学复杂系统研究所,太原030006 [2]中北大学数学系,太原030051

出　　处：《数学理论与应用》2023年第2期1-15,共15页Mathematical Theory and Applications

基　　金：国家重点研发计划(No.2018YFE0109600);国家自然科学基金(No.42075029)资助。

摘　　要：植被斑图是干旱半干旱区生态系统的典型特征之一,它能定性地刻画植被在空间上的分布结构,从而可作为生态系统改善和退化的早期指标.本文通过综述植被系统中存在的分支现象来揭示植被斑图的形成机制并提供荒漠化预警信号.首先,利用Hopf分支理论定性地分析植被系统产生空间齐次Hopf分支的条件,解释植被生物量呈现年际周期波动的现象.其次,利用Turing分支理论分析现有的植被模型,揭示植被的空间分布特征以及斑图的形成机制,并且运用多尺度分析方法细化这些斑图的类型以及寻找系统经历斑图相变的参数阈值.最后,当Hopf分支和Turing分支同时发生时,动力系统会经历Turing-Hopf分支.运用反应扩散方程的规范型理论推导Turing-Hopf分支的规范型,再通过柱坐标变换得到振幅方程,分析其动力学性态,进而揭示更复杂的植被时空斑图.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 TuringHopf bifurcation.By means of the normal form theory of reactiondiffusion equation,the normal form of the TuringHopf 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 arerevealed.

关 键 词：植被系统 HOPF分支 Turing分支 Turing-Hopf分支 

分 类 号：Q948[生物学—植物学] O175[理学—数学]