Rise and fall of periodic patterns for a generalized Klausmeier-Gray-Scott model
The paper addresses bifurcations and pattern formation in the Klausmeier system, which is the basic model for the ecological dynamics of semi-arid areas. It includes two equations of the reaction-diffusion type, one for the density of water, and the other for the biomass density. In the present work, the water equation is supplemented by a nonlinear diffusion term, which accounts for subterranean propagation of water. The pattern formation through Turing and Turing-Hopf bifurcations in this system is studied, and an effective complex Ginzburg-Landau equation is derived for this case. It is demonstrated that bifurcations are of the supercritical type. In the second part of the paper, a full Busse balloon, i.e., a full stability region for patterns with nonsmall amplitudes, is obtained in a numerical form. It is concluded that the desertification may be cause by various factors represented in the model by respective coefficients.
scientific article; zbMATH DE number 6143188
scientific article