On stochastic population model with the Allee effect

This paper discusses the existence, uniqueness and asymptotic stability of the solution to the stochastic population model with the Allee effect, which is represented by the stochastic differential equation d N t = N t ( 1 − N t T ) ( N t K − 1 ) ( r d t + α d W t ) . We are focused on the correlation between the growth rate r and population size N t , which is shown to be positive if the population size N t is above the Allee threshold T , and negative if N t < T .