具有偏利关系的随机三种群模型的动力学分析

Dynamics of Stochastic Three Populations Model with Partial-dvantage for Prey

研究一类具有偏利关系的随机三种群模型。证明系统的全局正解的存在唯一性、均值有界性,给出了种群灭绝与平均持续生存的条件,并证明了平稳分布的存在性。最后由理论结果和数值模拟可知:当噪声强度较大时,种群快速灭绝;当噪声强度较小时,种群减少速度变慢,并会持续生存。

A stochastic three populations model with partial-advantage for prey was studied. Firstly,the existence and uniqueness of the positive global solution starting from the positive initial value and the mean boundedness of the system were proved. Secondly,the sufficient conditions for the solution of population extinction and persistence in the mean were obtained,and the existence of stationary distribution under certain conditions was proved. Finally,the theoretical results and numerical simulations showed that the population would extinct as the enhancing of noise intensity,while the reductive speed of the population would slow down as the weakening of noise intensity,and the population would be persistent.