For a Depensatory Fishery System Hybrid Modeling and Optimal Control of Harvest Policies

Recent decades have brought an increasing concern for the sustainability of renewable resources, such as agricultural land, freshwater, forests, and fisheries. Management and control of them have been conducted through some institutions and governments, which mainly focus on efficiently managing those resources since they are affected by social and ecological uncertainties like climate change, difficulty in the application strategies, or uncertainties and noise in the data collection. Control engineering procedures represent a flexible and reasonable way to investigate and solve the difficulties, uncertainties, and noise listed above by formulating the problem mathematically. In this work, we investigate fisheries and revenue optimization by using a hybrid model. The harvest of the fishery is done during some seasons of the year, which suggests that the model should include both discrete and continuous dynamics. To investigate the bio-economic system, the problem is formulated by two-hybrid dynamical fishery models. Those formulations are used to investigate optimal control and the stability of the sustainability of the system. In this respect, we investigate the optimal effort for the maximization of the revenue where the continuation of sustainability is preserved. Moreover, which parameters should be taken into account to check the stability in this case are determined. Whenever the system is unstable, the optimal effort for the sustainability of the system is determined.