An analytical dynamic model of grass field ecosystem with two variables

An analytical dynamic model of grass field ecosystem is developed and analyzed. The model is a maximum simplified one, consisting of only two variables: the biomass of the grass field and the wetness of underlying soil. The other factors influencing the behaviour of macro-ecosystem, such as sunlight, temperature, precipitation, consuming and the physico-chemical properties of soil, are considered as known parameters in the model. The model is suitable for strict mathematical analysis and for demonstrating some major and essential features of the grass field ecosystem. It is revealed that the interaction between the grass biomass (plus coverage) and the evaporation (plus run off) is essential for determining the grass biomass of a possible ecological regime (the stable equilibrium state or limited cycle of the model). Namely, the biomass of a species interacting weakly with soil wetness continuously depends on the precipitation, while the biomass of a species interacting strongly with soil wetness is abundant if the precipitation is larger than some critical value, but is very small or zero if the precipitation is a subcritical one. More mathematical analysis of the model can probably yield further understanding of the ecosystem.