Dynamics of fisheries with prey reserve and harvesting

Abstract

A model for two fish species and one predator in a patchy environment is formulated using a deterministic model to study the dynamics of fishery in two homogeneous patches, a free fishing zone and a refuge for prey reserve in which fishing is prohibited. The system is analysed around steady states; the criteria for local and global stabilities are established. The existence of bionomic equilibrium of the system is determined and the conditions for their existence are derived. The optimal harvesting policy is studied by using Pontryagin's maximal principle. Sensitivity analysis is carried out and it is observed that the populations are more sensitive to growth, dispersal and predation rates, least sensitive to the catchability coefficient. Statistical analysis is employed to estimate the parameters and to assess both the uncertainty in the model parameters and in the model-based predictions. Graphical representations of the model are provided.

Dynamic Analysis of a Phytoplankton-Fish Model with the Impulsive Feedback Control Depending on the Fish Density and Its Changing Rate

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Bifurcation analysis of a modified Leslie–Gower model with Holling type-IV functional response and nonlinear prey harvesting

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An impulsive two-stage predator–prey model with stage-structure and square root functional responses

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