Stochastic dynamic balance of a bi-stable vegetation model with pulse control

The stochastic vegetation model with the pulse control is established, and the related dynamic mechanisms are explored. The stationary responses of the system can be detected by the stationary probability density function and the mean vegetation biomass. And the transient properties of the system are investigated by the mean first exit time of the attraction basin and the time series of the attractor. Due to the special discontinuity of the pulse control, these indexes are analyzed through numerical simulations alone. Specially, for the uncontrolled case, the analytical expressions of the stationary probability density and mean first exit time can be derived, and relative errors of the two proposed methods can be ignored as a whole. It turns out that the strong environmental disturbance such as the random climate change can influence the vegetation ecosystem balance, which can be effectively controlled by the pulse control.