INTERACTIONS OF TIME DELAY AND SPATIAL DIFFUSION INDUCE THE PERIODIC OSCILLATION OF THE VEGETATION SYSTEM

Empirical data exhibit a common phenomenon that vegetation biomass fluctuates periodically over time in ecosystem, but the corresponding internal driving mechanism is still unclear. Simultaneously, considering that the conversion of soil water absorbed by roots of the vegetation into vegetation biomass needs a period time, we thus introduce the conversion time into Klausmeier model, then a spatiotemporal vegetation model with time delay is established. Through theoretical analysis, we not only give the occurence conditions of stability switches for system without and with diffusion at the vegetation-existence equilibrium, but also derive the existence conditions of saddle-node-Hopf bifurcation of non-spatial system and Hopf bifurcation of spatial system at the coincidence equilibrium. Our results reveal that the conversion delay induces the interaction between the vegetation and soil water in the form of periodic oscillation when conversion delay increases to the critical value. By comparing the results of system without and with diffusion, we find that the critical value decreases with the increases of spatial diffusion factors, which is more conducive to emergence of periodic oscillation phenomenon, while spatial diffusion factors have no effects on the amplitude of periodic oscillation. These results provide a theoretical basis for understanding the spatiotemporal evolution behaviors of vegetation system.

Automated summary

Empirical data shows that vegetation biomass fluctuates periodically in ecosystems, and the mechanism behind this is related to the time it takes for soil water to be converted into vegetation biomass. Introducing conversion time into the model reveals that delay induces interaction between vegetation and soil water in the form of periodic oscillation. Comparing systems with and without diffusion, it is found that spatial diffusion factors affect the critical value for oscillation emergence, but not the amplitude.