The optimal strategy for a bioeconomical model of a harvesting renewable resource problem

In recent years, bioeconomics has seen fast development in different areas of natural resource modelling. In this paper, we study a bioeconomic model, where the control is the fishing effort variation rate, rather than the effort in the classical model of Clark, which can be interpreted as an investment. This consideration leads to a nonlinear problem of optimal control. We first establish a result on stability of the equilibrium point. We also obtain the optimal strategy of the model by applying the inductive method based on the verification functions.