A nonautonomous logistic population model with a feature of an Allee threshold has been investigated in a periodically fluctuating environment. A slow periodicity of the harvesting effort was considered and may arise in response to relatively slow fluctuations of the environment. This assumption permits obtaining the analytical approximate solutions of such model using the perturbation approach based on the slow variation. Thus, the analytical expressions of the population evolution in the situation of subcritical and the supercritical harvesting were obtained and discussed in the framework of the Allee effect. Since the exact solution was not available due to the nonlinearity of the system, the numerical computation was considered to validate our analytical approximation. The comparison between the two methods showed a remarkable agreement as the time progressed, while such agreement fell off when the time was close to the initial density. Moreover, in the absence of the periodicity of the harvesting term, the expressions of the population evolution reduced to the exact solutions but in implicit forms. The finding results were appropriate for a wide range of parameter values, which lead to avoiding extensive recalculations while displaying the population behavior.

A steady, laminar, and incompressible flow of Powell–Eyring fluid model over a linearly stretching sheet is numerically investigated in a porous, two-dimensional medium. An influence of a slip velocity phenomenon, magnetic field, viscous dissipation, heat source, and radiation on the fluid flowing are considered with this investigation. The governing equations for this scenario are derived and then transformed to be dimensionless using a suitable similarity. The set of equations is solved numerically utilizing bvp4c built–in solver in MATLAB^® software. To validate our results, a special case arising from this problem is obtained which shows a very good agreement with the previous studies. The effect of the considered physical quantities on the dimensionless velocity profile, temperature distribution, skin friction, and local Nusselt coefficient are described. Findings reveal that a resistance in the fluid flow and a growth in the thermal distribution have been noticed when the slip velocity phenomena, magnetic field, or permeability parameter is increased, whereas enhancing the velocity profile and thermal distribution can markedly be seen by increasing the radiation magnitude.