Dynamics of a stochastic impulsive vegetation system with regime switching

Abstract

This paper describes an analytical and numerical investigation of a novel stochastic impulsive vegetation system with regime switching. Impulsive control, white noise, regime switching, and rainfall are modeled as crucial factors to simulate natural ecological phenomena, with the aim to explore the effects of those factors on the dynamics of vegetation system. Dynamics of the system, including the existence and uniqueness of global positive solutions, extinction, non-persistence in the mean, weak persistence and stochastic persistence, are investigated firstly under the effects of impulsive control and regime switching. For system without impulsive perturbations, we investigate the existence and uniqueness of the stationary distribution for the system, demonstrating that the vegetation can survive forever. Using a sophisticated sensitivity analysis technique, it is found that the vegetation biomass is highly sensitive to the rainfall but least sensitive to the saturation constant of the vegetation consumption. Our numerical results reveal that either the reduced rainfall or increased environmental disturbance can tip the balance of vegetation system, but this relationship can be effectively regulated by implementing impulsive control schemes. Additionally, it is observed that system at high-level rainfall may be detrimental to maintain the balance of vegetation, but regime switching in rainfall patterns can balance different states of vegetation and provide higher survival chance for vegetation. Significantly, it emphasizes that the persistence-extinction behaviors of the vegetation are more sensitive to the change of regime switching, indicating that the proper and general environmental disturbances is beneficial to maintain dynamic balance of vegetation system. These findings may provide new insights into the complex vegetation system dynamics.