ANALYSIS OF A STOCHASTIC TREE-GRASS MODEL WITH MEAN-REVERTING ORNSTEIN-UHLENBECK PROCESS

Considering the survival regulation mechanisms of trees and grasses in savannas ecosystems, the stochastic variability of ecosystems and the effects of fire, a stochastic tree-grass model with mean-reverting Ornstein-Uhlenbeck process is developed and investigated in this paper. Firstly, the biological and environmental components of the tree-grass model and the biological significance of each parameter are described, while the mean-reverting Ornstein-Uhlenbeck process is introduced and its biological significance is explained. Then we list some dynamical properties of the model and give proofs. The existence and moment estimates of the global solution of the stochastic model and sufficient conditions for the existence of a stationary distribution are given. In addition, we give sufficient conditions for extinction of species. Finally, we verify that the theories are valid by numerical simulation.