Dynamics of competition model between two plants based on stoichiometry

Abstract

The dynamics of two-plant competitive models have been widely studied, while the effect of chemical heterogeneity on competitive plants is rarely explored. In this study, a model that explicitly incorporates light and total phosphorus in the system is formulated to characterize the impacts of limited carbon and phosphorus on the dynamics of the two-plant competition system. The dissipativity, existence and stability of boundary equilibria and coexistence equilibrium are proved, when the two plants compete for light equally. Our simulations indicate that, with equal competition for light ($ b_{12} = b_{21} $) and a fixed total phosphorus in the system ($ T $), plants can coexist with moderate light intensity ($ K $). A higher $ K $ tends to favor the plant with a lower phosphorus loss rate ($ d_1 $ vs $ d_2 $). When $ K $ is held constant, a moderate level of $ T $ leads to the dominance of the plant with a lower phosphorus loss rate ($ d_1 $ vs $ d_2 $). At high $ T $ levels, both plants can coexist. Moreover, our numerical analysis also shows that, when the competition for light is not equal, the low level of total phosphorus in the system may lead the model to be unstable and have more types of bistability compared with the two-dimensional Lotka-Volterra competition model.

Keywords

• stoichiometric system
• competition model
• nutrient limitation
• bistability
• bifurcation