Some simplified dynamic models of grass field ecosystem are developed and investigated. The maximum simplified one consists of two variables, living grass biomass and soil wetness. The analyses of such models show tha...Some simplified dynamic models of grass field ecosystem are developed and investigated. The maximum simplified 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.展开更多
Based on general consideration and analysis, a maximum simplified dynamic model of grass field ecosystem with a single species is developed. The model consists of two variables: grass biomass of grass field per unit a...Based on general consideration and analysis, a maximum simplified dynamic model of grass field ecosystem with a single species is developed. The model consists of two variables: grass biomass of grass field per unit area and soil wetness, and is suitable for describing their mutual interaction. Other factors such as physical-chemical characteristics of soil, precipitation, irrigation, sunlight, temperature and consumers, are taken into account as parameters in the dynamical system. Qualitative analysis of the model shows that grass biomass of a possible ecological regime is determined by the stable equilibrium state of the dynamical system. For the grass species interacting weakly with soil wetness the grass biomass continuously depends on the precipitation. While, for a species interacting strongly with soil wetness, grass biomass is abundant if precipitation is larger than some critical value; otherwise, it becomes a desertification regime with very little or even zero grass biomass. The model also shows that there exists a critical (maximum) consuming value, the grass field with abundant biomass can be restored if the consuming is less than the critical value; otherwise, it becomes desertification.展开更多
文摘Some simplified dynamic models of grass field ecosystem are developed and investigated. The maximum simplified 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.
文摘Based on general consideration and analysis, a maximum simplified dynamic model of grass field ecosystem with a single species is developed. The model consists of two variables: grass biomass of grass field per unit area and soil wetness, and is suitable for describing their mutual interaction. Other factors such as physical-chemical characteristics of soil, precipitation, irrigation, sunlight, temperature and consumers, are taken into account as parameters in the dynamical system. Qualitative analysis of the model shows that grass biomass of a possible ecological regime is determined by the stable equilibrium state of the dynamical system. For the grass species interacting weakly with soil wetness the grass biomass continuously depends on the precipitation. While, for a species interacting strongly with soil wetness, grass biomass is abundant if precipitation is larger than some critical value; otherwise, it becomes a desertification regime with very little or even zero grass biomass. The model also shows that there exists a critical (maximum) consuming value, the grass field with abundant biomass can be restored if the consuming is less than the critical value; otherwise, it becomes desertification.
