生态脆弱区生态系统状态演变分析的若干数学方法

Mathematical methods for analyzing ecosystem state evolution in ecologically vulnerable area

生态脆弱区往往存在多个生态系统(草原、荒漠和灌木等)共存的现象。由于外部环境和人类活动等因素的影响,生态脆弱区会发生从一种生态系统转变为另一种生态系统的现象,即突变现象。分析生态脆弱区多生态系统共存情况下生态系统的稳定性对了解生态脆弱区生态系统的变化具有重要意义。本文回顾了目前能够描述生态脆弱区多生态系统的动力系统及其稳定性判别的若干数学方法。基于微分方程的动力系统不仅能够描述均一和非均一的生态系统,而且能够描述林、草和荒漠等多生态系统共存的状态。判别生态脆弱区生态系统稳定性的方法包含3类:第一类是代表人类活动等因素变化的初值扰动引起的生态系统稳定性的分析方法;第二类是代表环境因子(例如降水和温度)等因素变化的模式扰动引起的生态系统稳定性的分析方法;第三类是由初值扰动和模式扰动共同作用引起的生态系统稳定性的分析方法。最后,介绍了应用上述方法分析生态脆弱区多生态系统的稳定性。这些数学理论方法不仅有助于我们了解生态脆弱区生态系统的稳定性,而且也可为生态脆弱区生态系统的突变、预估和管理提供理论指导。

Multiple ecosystems(grassland,desert and shrubs)always coexist in ecologically fragile areas.Influence by external environmental conditions and human activities,one ecosystem in ecologically fragile areas would be changed into another,called abrupt change.It is important to analyze the stability of each ecosystem in ecologically fragile areas under the condition of multiple ecosystems coexistence for understanding ecosystem changes.In this article,we reviewed several mathematical models that can describe the dynamic system and stability of multiple ecosystems in ecologically fragile areas.The dynamic system described by differential equations included the uniform and non-uniform ecosystems,as well as multi-ecosystems with the existence of forests,grasses,and deserts.There were three types of methods for analyzing the stability of the ecosystem.One type was the analysis method of ecosystem stability caused by the initial perturbation that could represent human activities,and the other type was the analysis method of ecosystem stability caused by the model perturbation that can represent the changes of environmental factors(precipitation,temperature,etc.),and the third type was the analysis method of ecosystem stability caused by the combination of initial perturbation and model perturbation.Finally,we introduced how to analyze the stabilities of ecosystem in ecologically fragile areas with those methods.These mathematical methods not only help us understand the stability of the ecosystems in the ecologically fragile area,but also provide theoretical guidance for the abrupt change of the ecological system,future prediction,and management.