A system of impulsive stochastic differential equations is proposed as a two-species facultative mutualism model subject to impulsive and two coupling noise source perturbations, in which the saturation effect is taken into account. A set of sufficient criteria for extinction (exponential extinction and extinction) and permanence (permanence in time average and stochastic permanence) of the system are established. Extensive simulation figures are demonstrated to support the theoretical findings. Meanwhile, we look at the effects of coupling white noises, impulses, intrinsic growth rates, intra-specific competition rates and inter-specific mutualism rates on the survival of populations.

中文翻译：

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具有饱和效应的脉冲随机兼性共生系统的生存分析

提出了一个脉冲随机微分方程系统，作为一种受脉冲和两个耦合噪声源扰动的两种兼性共生模型，其中考虑了饱和效应。建立了一套系统的消光（指数消光和消光）和持久性（时间平均持久性和随机持久性）的充分标准。广泛的模拟数据被证明来支持理论发现。同时，我们研究了耦合白噪声、脉冲、内在增长率、种内竞争率和种间共生率对种群生存的影响。