Effects of stochastic perturbations on the tree–grass coexistence in savannas.

Savannas are widely distributed on the earth, and the growth of plants in savannas often encounters the environmental perturbations. In this research, based on a deterministic tree–grass savanna model proposed by Tamen et al. (Biomath 3: 1407191, 2014), we use white noise and a continuous-time Markov chain to model the slight environmental perturbations and environmental regime switching, respectively, and formulate a stochastic tree–grass savanna model under regime switching. We first give conditions under which the model is permanent (i.e., the tree species and the grass species coexist) in the sense that the model admits a unique ergodic non-boundary stationary distribution and the transition probability of the solution of the model converges to this stationary distribution exponentially under total variation norm. Then, we provide conditions under which the grass species or the tree species die out. Finally, we discuss the impacts of random environmental perturbations on the coexistence and disintegration of the model with the help of exemplary data and numerical simulations. [ABSTRACT FROM AUTHOR]