Two-variable dynamic model of grass field ecosystem with seasonal variation

The seasonal variation of meteorological elements such as temperature and precipitation leads to the seasonal cycle of parameters included in the dynamic model of grass field ecosystem. Our results show that there exist periodic solutions of the two-variable dynamic model of grass field ecosystem developed in our previous paper, provided the parameters of the model undergo periodic seasonal variation. Every integral curve coincides with or eventually approaches an associated periodic solution. Bifurcation exists if the correspondent model with no seasonal variation possesses two or more equilibrium points, but the line(s) of bifurcation is (are) different from that (those) for the model with no seasonal variation. This means that the periodic solutions associated with either a regime of rich grass biomass or a regime of desertification are stable in respect to the disturbances which are generated by other factors and which are not too large. However, a large enough disturbance can result in a transition to very different ecological regime. The model explains the mechanism of local desertification due to the overuse of grass field. The numerical results also give a hint on how many seasonal cycles (years) are needed for establishing a grass field with rich grass biomass if the initial grass biomass or soil wetness is not large enough.