环境噪声对具有捕获的种群竞争系统的影响

Influence of Environmental Noises on Competiveness with the Harvesting Population Model

运用色噪声刻画环境变化性构造了随机的具有捕获的两种群竞争的Gompertz模型,讨论了环境变化和人工捕获对种群生长过程的影响.通过求解在平衡点处线性化的随机微分方程,计算出了两种群偏离平衡点处的期望和方差,研究得到环境随机性虽然会导致种群密度随机变化,但随着时间的增长,种群的密度变化只可能在平衡状态处摆动.最后还讨论了为减少两种群灭绝可能性,系统保持稳定的参数域.

In this article,we characterize the environment variation with the color noise and construct the stochastic Gompertz model with two populations competing for harvesting.By solving the Linearity stochastic differential equation in the equilibrium,we calculate the expectation and the variance of the two species deviating the equilibrium.At last,we come to the conclusion that,despite the fact that environmental randomness affects the population density,the populations’ growth only fluctuates around the equilibrium as the time elapses.In the end,we estimate the safe parametric space for the purposes of reducing the likelihood of extinction of the species to the minimal.