Population Growth of Small Harmful Rats in Grassland Subjected to Noise

The population growth of small harmful rats in grassland subjected to environment fluctuation has been modelled in a logistic equation. Two correlated random variables responsible to the fluctuation of the genetic factor and the suppression factor are used. A two-peak structure of the steady probability distribution of rate population is observed in the large fluctuation regime of the genetic factor. With the increase of correlation constant λ, the steady probability distribution can change from two peaks to a single peak. The suppression factor μ and its fluctuation also affect the steady
probability distribution and can push it toward a small population.