AN ANALYTICAL DYNAMIC-MODEL OF GRASS FIELD ECOSYSTEM WITH 2 VARIABLES

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.