Multistability shifts in an aird vegetation system with nonlocal water absorption effect

In arid regions, the distribution of vegetation often exhibits rich and diverse patterning phenomena. Typically, the pattern structure is characterized by a single periodic state known as the Turing pattern. Recent research on the interaction between vegetation and water has overlooked the fact that vegetation can absorb water from the entire space, not just its immediate location. To address this, we develop a vegetation-water model incorporating a nonlocal water absorption effect, present the conditions for Turing bifurcation occurrence, and derive the amplitude equation along with the generation conditions for subcritical bifurcation through weakly nonlinear analysis. Our findings demonstrate that introducing a nonlocal water absorption strength can lead to the emergence of a supercritical Turing bifurcation when the water diffusion coefficient is small, as opposed to being limited to a subcritical type. Moreover, this nonlocal effect plays a critical role in the transition of the Turing bifurcation from supercritical to subcritical, resulting in the coexistence of multiple stability states in the snaking region. These multistability states correspond to pattern structures observed in Senegal, which differ from fairy circles (the typical Turing pattern) in Australia. Additionally, our results show that the vegetation system transitions from monostability at low precipitation to bistability at high precipitation, passing through intermediate states of bistability and tristability. The tristability state consists of bare soil (BS), uniform vegetation (UV), and periodic pattern (PP), while the bistable state comprises two stability states. In summary, these findings offer new perspectives on studying the impacts of the nonlocal water absorption effect on multistability shifts and the spatiotemporal distribution patterns of vegetation ecosystems.