The impact of heterogeneous human activity on vegetation patterns in arid environments

Steady-state bifurcation and spike pattern in the Klausmeier-Gray-Scott model with non-diffusive plants

“…Some extended models describing the interactions between surface water, soil water, and plants were derived by distinguishing the water on top of the soil and the water penetrated into the soil [7,8,14,45]. Furthermore, on the basis of these models, the researchers considered the influence of some external factors on vegetation patterns, such as climate change [4,12,25,53], heterogeneous human activity [15], and nonlocal grazing [36,50,51]. The review [53] investigated the main climatic factors affecting vegetation patterns and their impact on pattern structures and ecological functions in terms of mathematical modeling and data analysis.…”

“…The review [53] investigated the main climatic factors affecting vegetation patterns and their impact on pattern structures and ecological functions in terms of mathematical modeling and data analysis. Hou et al [15] found that the spatiotemporal heterogeneity of human activities increases the diversity of pattern structures through optimal control theory. In addition, Ge [5] found that the vegetation Turing pattern exhibits the hyperuniformity from a longrange perspective, and its degree is positively related to the water-use efficiency of the vegetation.…”

“…It is easy to see that the characteristic equation ( 15) has a zero root when d = d O n . Differentiating (15) with respect to d, we obtain the transversal condition dλ(n, d)…”