Multiscaling analysis of a slowly varying single species population model displaying an Allee effect (Q2875731)

The authors consider the dynamics of a single species population which grows in a logistic fashion, while being also subject to an Allee effect. Assuming that the model parameters are slowly varying functions of time, a multiscaled perturbation analysis based on two time scales is performed to give analytic approximations of the solution. Although these approximations are given in an implicit form this form is relatively simple and easily representable, a good agreement between the leading order approximation and the numerical approximation being observed for a wide range of initial populations.