In this paper, we establish a stochastic dynamical grazing ecosystem with time delays and fluctuations. The effects of time delay, Gaussian noise and Lévy noise on the stationary probability distribution (SPD), the mean first passage time (MFPT) and stochastic resonance (SR) are analyzed. Our research results show the following: (i) For small time delay, the increasing Gaussian noise intensity leads to catastrophic regime shift (CRS) from high vegetation state to low vegetation state, while the increasing Lévy noise intensity contributes to the recovery of these shifts. For large time delay, the increasing Gaussian noise intensity or Lévy noise intensity causes the CRS phenomenon, the larger the time delay, the more frequent the CRS phenomenon. (ii) The increasing Gaussian noise intensity can diminish the stability of the high vegetation state and low vegetation state, the increasing Lévy noise intensity and Lévy stability index can enhance the stability of the high vegetation state and diminish the stability of the low vegetation state. The increasing Lévy noise intensity can lead to noise-enhanced stability (NES) of the high vegetation state, and the larger the time delay, the more pronounced the NES phenomenon. (iii) The increase of time delay can weaken SR phenomenon when signal-to-noise ratio (SNR) is a function of Gaussian noise intensity and Lévy noise intensity.

在本文中，我们建立了一个具有时间延迟和波动的随机动态放牧生态系统。分析了时延、高斯噪声和Lévy噪声对平稳概率分布(SPD)、平均首次通过时间(MFPT)和随机共振(SR)的影响。我们的研究结果表明：（i）对于小时间延迟，高斯噪声强度的增加会导致从高植被状态到低植被状态的灾难性政权转变（​​CRS），而Lévy噪声强度的增加有助于这些转变的恢复。对于大时延，高斯噪声强度或Lévy噪声强度的增加会引起CRS现象，时延越大，CRS现象越频繁。(ii) 高斯噪声强度的增大会减弱高植被状态和低植被状态的稳定性，Lévy噪声强度和Lévy稳定性指数的增大会增强高植被状态的稳定性，减弱低植被状态的稳定性。Lévy噪声强度的增加会导致高植被状态的噪声增强稳定性（NES），并且时间延迟越大，NES现象越明显。(iii) 当信噪比(SNR)是高斯噪声强度和Lévy噪声强度的函数时，时间延迟的增加会减弱SR现象。