First escape probability and mean first exit time for a time-delayed ecosystem driven by non-Gaussian colored noise

The first escape probability (FEP) and the mean first exit time (MFET) are utilized to explore the stability of the high vegetation basin in an extended ecosystem with the two important features: the randomness and the delay. The more realistic non-Gaussian colored noise is chosen as a stochastic perturbation. In order to overcome the effects of the system inherent parameters, two novel basin stability indexes are proposed based on the FEP and the MFET. The unified colored noise approximation and the small delay approximation are exploited to further simplify the system and obtain the stability indexes. The results show that either increased herbivores or reduced rainfall can increase the FEP and decrease the MFET of the high vegetation ecosystem, and non-Gaussian colored noise disturbance also exacerbates the problem. Conversely, the time delay can control deterioration of the ecosystem. Furthermore, by comparing the theoretical analysis results and Monte Carlo simulation results of the original system, it is found that both the approximation methods and the process of solving the FEP and the MFET are feasible.