An analytical dynamic model of grass field ecosystem is developed and
analyzed. The model is a maximum simplified one, consisting of only tw
o variables: the biomass of the grass field and the wetness of underly
ing soil. The other factors influencing the behaviour of macro-ecosyst
em, such as sunlight, temperature, precipitation, consuming and the ph
ysico-chemical properties of soil, are considered as known parameters
in the model. The model is suitable for strict mathematical analysis a
nd for demonstrating some major and essential features of the grass fi
eld ecosystem. It is revealed that the interaction between the grass b
iomass (plus coverage) and the evaporation (plus run off) is essential
for determining the grass biomass of a possible ecological regime (th
e stable equilibrium state or limited cycle of the model). Namely, the
biomass of a species interacting weakly with soil wetness continuousl
y depends on the precipitation, while the biomass of a species interac
ting strongly with soil wetness is abundant if the precipitation is la
rger than some critical value, but is very small or zero if the precip
itation is a subcritical one. More mathematical analysis of the model
can probably yield further understanding of the ecosystem.