We consider an adaptation of the well-known logistic equation in mathematical ecology in which the population is assumed to diffuse and for which the average growth rate is a function of some specified delayed argument. Using a combination of analytical and numerical techniques, we investigate the existence, uniqueness, and asymptotic stability of the nonnegative steady states of this equation.
Davidson, F. A., & Gourley, S. A. (2001). The effects of temporal delays in a model for a food-limited diffusing population. Journal of Mathematical Analysis and Applications, 261(2), 633-648. https://doi.org/10.1006/jmaa.2001.7563