Optimal Management of a Renewable Resource Subjected to Strong Allee effect in a Periodically Fluctuating Environment

Abstract

In this article we present the qualitative properties of solutions of a periodic differential equation that describes dynamics of a renewable resource subjected to strong Allee effect (multiplicative Allee effect) with periodic harvesting in a periodically fluctuating environment. We also present the bio-economic aspects of the considered renewable resource studied from sole owner perspective. An optimal harvesting problem with periodic dynamic constraints has been solved using Pontryagin’s maximum principle. It is interesting to find that the considered optimal control problem admits multiple periodic singular solutions. Techniques are developed to identify the optimal singular solution and the associated optimal singular periodic effort function. Optimal, suboptimal harvest policies and their corresponding approach paths are constructed. It is found that the optimal harvest policies are periodic after some time.