Abstract
Based on the physical analysis that the soil moisture and vegetation depend mainly on the precipitation and evaporation as well as the growth, decay and consumption of vegetation a nonlinear dynamic coupled system of soil moisture-vegetation is established. Using this model, the stabilities of the steady states of vegetation are analyzed. This paper focuses on the research of the vegetation catastrophe point which represents the transition between aridness and wetness to a great extent. It is shown that the catastrophe point of steady states of vegetation depends mainly on the rainfallP and saturation value v0, which is selected to balance the growth and decay of vegetation. In addition, when the consumption of vegetation remains constant, the analytic solution of the vegetation equation is obtained.
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