Finite-time stability of a stochastic tree–grass–water–nitrogen system with impulsive and time-varying delay

Abstract

A class of time-varying delay impulsive reaction–diffusion tree–grass–water–nitrogen system driven by Lévy jump process is considered. First, we prove the existence and uniqueness of the global positive solution of the model by constructing the Lyapunov function. Secondly, several sufficient conditions for finite-time stability are given by using comparison theorem and mean impulse interval method. Finally, numerical simulations are carried out to verify the effectiveness of the theoretical analysis.