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Abstract: Considering the impact of harvesting on the coexistence and competitive exclusion of competitive predators, a two-zooplankton one-phytoplankton model with harvesting is proposed and investigated. First, stability criteria of the model is analyzed both from local and global point of view. Second, two types of zooplankton will competitively exclude each other in the absence of harvesting with the zooplankton with the larger threshold persisting. If harvest rates are discriminate, then a dominant zooplankton may occur depending on the harvesting level. Thus, for some harvesting levels, the zooplankton one may persist while for other harvesting levels zooplankton two may persist. Furthermore, the value of the harvesting level and coexistence line are obtained when coexistence occur. Finally, the impact of harvesting is mentioned along with numerical results to provide some support to the analytical findings. [Copyright &y& Elsevier]

Abstract: This paper deals with a predator–prey model with specialist harvesting, representing a two predators (Zooplankton) and one resource (Phytoplankton) system. First, the existence and stability of equilibria is analyzed both from local and global point of view. Our results indicate that a specialist harvesting which is discriminate may mediate the coexistence of the two zooplankton species which competitively exclude each other in absence harvesting. Although in most cases increasing harvesting reduces the two zooplankton species numbers, when harvesting leads to coexistence, it may also lead to increase the two zooplankton species numbers. Furthermore, to protect fish population from over exploitation a control instrument tax is imposed. The problem of optimal taxation policy is then solved by using Pontryagin’s maximal principle. It is established that the zero discounting leads to the maximization of the net economic revenue to the society and an infinite discount rate leads to complete dissipation of the net economic revenue to the society. Finally, the impact of harvesting is mentioned along with numerical results to provide some support to the analytical findings. [Copyright &y& Elsevier]

Abstract: Considering that over exploitation would result in the extinction of the population, we propose and investigate a Holling II functional response prey-predator model with harvesting for fishery resource in a two-patch environment: a free fishing zone (patch 1) and a reserve zone (patch 2) where fishing is strictly prohibited. First, the presence of harvesting can impact the existence of equilibria. Further, stability criteria of the model is analyzed both from local and global point of view. Our results indicate that so long as the prey population in the reserved zone does not extinct, the both prey always exist, that is marine reserves should ensure the sustainability of system. Thus, marine reserves not only protect species inside the reserve area but they can also increase fish abundance in adjacent areas. Next, the existence of bionomic equilibrium and the optimal harvesting policy are discussed. The present value of revenues is maximized by using Pontryagin’s maximum principle. It is established that an infinite discount rate leads to complete dissipation of economic rent. Finally, some numerical simulations are given to illustrate our results. [Copyright &y& Elsevier]