种内竞争时滞对植被周期振荡模式的影响研究

考虑到干旱、半干旱地区的幼年植被与成年植被之间存在竞争水资源的现象，该文构建一个具有种内竞争时滞的植被-土壤水动力学模型。分析出系统存在植被灭绝平衡点和植被生存平衡点，并给出了平衡点局部稳定的条件，分别给出非空间系统和空间系统产生Hopf分支周期解的条件。通过数值模拟展示出两种系统对应的植被随时间演化做周期振荡模式，并通过参数敏感性分析发现降雨量和植被的增长率对这种模式的产生和模式的振幅、周期有显著影响，但蒸发量的影响效果最不显著，表明降雨量和植被本身的特征对干旱、半干旱地区植被的演化发展产生了深刻的影响。同时发现空间扩散的引入会抑制这种模式的发生，但对振幅和周期没有任何影响。所获得的结果解释了自然界中广泛观察到的植被周期振荡现象，为植被系统的可持续发展提供了理论支撑。

Effects of Intraspecific Competition Delay on Vegetation Periodic Oscillation Patterns

Aimed at the phenomenon of competing for water resources between young vegetation and adult vegetation in arid and semi-arid areas, a vegetation-soil water dynamic model with intraspecfic competition delay was established. The conditions for the existence of an unique vegetation survival equilibrium and the local stability of the vegetation extinction equilibrium were analyzed. The generating conditions for Hopf bifurcating periodic solutions of non-spatial and spatial systems were given, respectively. The periodic oscillation pattern appearing in the vegetation evolution with time was numerically simulated. Through the parameter sensitivity analysis, the rainfall and the vegetation growth rate were found to have significant influences on the generation, the amplitude and the period of this pattern, while the effects of evaporation was found to be the least significant. The results indicate that, the rainfall and the vegetation properties have profound impacts on the evolution and development of vegetation in arid and semi-arid areas. The introduction of spatial diffusion inhibits the occurrence of this pattern, but doesn’t affect the amplitude and the period. The work explains the phenomenon of vegetation periodic oscillation widely observed in nature, and provides theoretical supports for the sustainable development of the vegetation system.