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From the standpoint of fishery management, an essential component of the basic information upon which policy can be based consists of intelligence from field data and computations. In certain situations, these studies can provide quite a great deal of the necessary information. However, in other situations they have not been able to give unequivocal answers to important questions, especially where several influential factors are involved in the whole jigsaw of the complex fishery system, in which their relative abundance may vary with the intensity of the recruitment effort or with spatial migration. Here, we propose and analyze a reaction–diffusion model for the fish population incorporating time-dependent fishery intensity. Using the traveling wave coordinate, we derive analytical solutions to the model system. Conditions on the system parameters are derived which ensure stability of the system under study. Phase portrait and traveling wave solution are plotted and discussed in order to gain better insights into the spatial movement of the fish population in time.

Stability analysis and traveling wave solution of a reaction–diffusion model for fish population incorporating time-dependent recruitment intensity