Simplified Dynamic Models of Grass Field Ecosystem

Abstract: Some simplified dynamic models of grass field ecosystem are developed and investigated. The maximum simpli-fied one consists of two variables, living grass biomass and soil wetness. The analyses of such models show that there exists only desert regime without grasses if the precipitation p is less than a critical value pc; the grass biomass continuously depends on p if the interaction between grass biomass and the soil wetness is weak, but the strong interaction results in the bifurcation of grass biomass in the vicinity of pc; the grass biomass is rich as p > pc, but it becomes desertification as p < pc. Periodic solutions also exist in the model, if the seasonal cycle of model’s parameters is introduced. An improved model consists of three variables, i.e. the living grass biomass x, the nonliving grass biomass accumulated on the ground surface y and the soil wetness z. The behaviours of such three variables model are more complicated. The initial values of y and z play a very important role.

Keywords:
• Dynamic model,
• Grass field ecosystem,
• Bifurcation