Abstract
The stochastic stability for the irregular attraction basin in a time-delayed vegetation-water ecosystem disturbed by Lévy noise is explored. We first discuss that average delay time does not change the attractors of the deterministic model but affects the corresponding attraction basins, and we present the generation of Lévy noise. Then, we investigate the influence of stochastic parameters and delay time on the ecosystem by two statistical indicators, the first escape probability (FEP) and the mean first exit time (MFET). The numerical algorithm for calculating the FEP and the MFET in the irregular attraction basin is implemented, which is effectively verified by Monte Carlo simulations. Furthermore, the metastable basin is defined by the FEP and the MFET and confirms the consistency of the two indicators reflecting results. The result shows that the stochastic stability parameter, especially the noise intensity, decreases the basin stability of the vegetation biomass. In this environment, the time delay effect can validly alleviate its instability.
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