Abstract
The logistic equation has been used to model a population where the intrinsic rate of growth is a linearly decreasing function of the population density. We propose some models arising from discretizations of perturbed logistic equation where external factors such as harvesting and migration are included. The different discretizations exhibit diverse dynamic asymptotic behavior when dependence on two control parameters are allowed. We also give an alternative method to provide with new models that produce better approximating solutions.