Dynamics and optimal harvesting of prey-predator fishery models in the presence of a toxicant using pontryagin maximum principle - Ang, Tau Keong (2020)
In this thesis, several harvested fishery models using various types of harvesting strategies including the common harvesting, independent harvesting and nonlinear Michaelis-Menten harvesting functions are presented and analyzed. Besides that, most of the models are taking the existence of a toxicant into consideration, either in an anthropogenic or a self-produced form. In order to account for the intraguild predation interaction that occurs in marine ecosystems, three species fishery models are also studied by modeling the carrying capacities of both intraguild prey and predator fish as time-dependent variables. The idea of variable carrying capacity tends to describe the fish population dynamics in a varying environment by assuming their growth to be dependent on the environmental resource availability. In the context of resource management, an optimal harvesting policy is derived for the proposed models that aims to attain an optimal and sustainable yield of harvesting fisheries. Recent studies reveal that the study of harvesting alone is not sufficient to provide qualitative insights into the intrinsic behaviors of marine fish populations subject to harvesting. In fact, some of the important elements such as the presence of toxicants and intraguild prey-predation, as well as the interplay of the population with surrounding environment, are often neglected in most of the current studies. Therefore, the main contribution of this thesis is to generate insights into the dynamical behaviors of fishery models that account for the combination of the existence of harvesting, toxicant, as well as intraguild predation interaction. The dynamical properties discussed in this thesis give better understanding of the maximum thresholds of harvesting before the fish populations are driven to extinction. This thesis serves as a platform to investigate the optimal tradeoff of harvesting fisheries