一类随机互惠模型的渐近性质

Asymptotic properties of a stochastic mutualism model

针对一类具有饱和项和毒素影响的两种群互惠模型,考虑在外界白噪声扰动下相应的随机两种群互惠模型。利用随机微分方程的基本理论以及一些不等式技巧,得到此随机两种群互惠模型解的全局存在唯一性、随机有界性、随机持久性、随机灭绝性、全局吸引性和样本轨道估计等种群动力学性质。数值模拟验证了所得的结论。

For a stochastic two-species mutualism model with the saturation and toxin effect, its stochastic two-species mutualism model with white noise perturbation is investigated. Applying theory of stochastic differential equations and some inequalities, some population dynamical properties including the existence of global positive solutions, stochastic boundedness, stochastic permanence, stochastic extinction, global attractivity and pathwise estimation are obtained. Some numerical simulations complement analytical findings.