Abstract
A mathematical model describing a single species fishery is presented. The coupling effect of intra-species interaction delay of the harvested species and the spatial non-homogeneity of the aquatic environment is studied. The analysis is performed in a finite domain with the help of Neumann boundary value problem which resembles a closed-habitat fishery. Existence, uniqueness and regularity of solutions are demonstrated using the method of upper-lower solution pair. Stability criteria of the system is derived and interpreted from a bio-economic viewpoint.
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