EFFECT OF NONLOCAL DELAY WITH STRONG KERNEL ON VEGETATION PATTERN

In order to understand the mechanism of water uptake by vegetation, we propose a vegetation-water model with nonlocal effect which is characterised by nonlocal delay with strong kernel in this paper. By mathematical analysis, the condition of producing steady pattern is obtained. Furthermore, the amplitude equation which determines the type of Turing pattern is obtained by nonlinear analysis method. The corresponding vegetation pattern and evolution process under different intensity of nonlocal effect in roots of vegetation are given by numerical simulations. The numerical results show that as intensity of nonlocal effect increases, the isolation degree of vegetation pattern increases which indicates that the robustness of the ecosystem decreases. Besides, the results reveal that with the water diffusion coefficient increases, the change of pattern structure is: stripe pattern$ \rightarrow $mixed pattern$ \rightarrow $spot pattern. Our results show the effects of diffusion coefficient and intensity of nonlocal effect on vegetation distribution, which provide theoretical basis for the study of vegetation.