Abstract
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 .
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