Consolo, Giancarlo ， Grifo, Gabriele
2025-02-01 RICERCHE DI MATEMATICA 2025 74(卷), 1(期), (235-247页)
Turing vegetation patterns in flat arid environments are investigated in the framework of a modified version of the Klausmeier model in which finite soil carrying capacity is taken into account. The role of such a quantity is elucidated by means of linear and weakly-nonlinear stability analyses, that allow to characterize the key dynamical features associated to patterned solutions at and close to onset. The analytical predictions are also corroborated via numerical investigations which also provide a means to analyze some critical ecological scenarios, such as transition toward desertification, that can be observed when the soil carrying capacity undergoes variations over time.