Dynamic analysis of a plant-water model with spatial diffusion

Vegetation pattern is one of the typical features in arid or semi-arid areas and thus revealing the mechanism of vegetation evolution is helpful to understand the behavior of ecosystem. To this end, we investigate the spatiotemporal dynamics of a diffusive plant-water model in an arid flat environment in this paper. By carrying out bifurcation analysis, we find that the system has the properties of Turing-Hopf bifurcation. Based on the normal form theory of reaction-diffusion equations, the dynamics of the diffusive plant-water model in the neighbourhood of the Turing-Hopf bifurcation point are exactly analyzed. Our results show that tiny changes of parameters can induce the switch of four different states including uniform state, time periodic state, spatially inhomogeneous steady state and spatially inhomogeneous periodic state. Moreover, there are different types of bistable phenomenon between desert state and other states, which will provide some insights into that whether ecosystems are vulnerable. (C) 2022 Elsevier Inc. All rights reserved.

Automated summary

The study investigates the spatiotemporal dynamics of a diffusive plant-water model in an arid flat environment and finds that the system exhibits Turing-Hopf bifurcation properties. By analyzing the normal form theory of reaction-diffusion equations, the study reveals that tiny changes in parameters can induce the switch between different states, including uniform state, time periodic state, spatially inhomogeneous steady state, and spatially inhomogeneous periodic state.