Qualitative analysis of a stock-effort parabolic model incorporating marine reserve

Abstract

A stock-effort dynamical model of a fishery with spatial structure is considered to assess the impacts of reserve size on fishing catch. We study the existence, uniqueness and global character of the solutions. It is shown that when the cost of fishing effort is less than the principal eigenvalue for an elliptic operator defined on a bounded domain corresponding to the fishing zone, then the fishery is viable, while in the opposite case, the fishery is not viable and fishing effort disappears. For both cases, the existence of stable solutions is studied. We perform some numerical simulations to illustrate our results in this paper and give a brief concluding remark.

Keywords:

• Reaction–diffusion models
• fishery models
• protection zone

AMS subject classifications:

• 92B05
• 92D25
• 92F99

Disclosure statement

No potential conflict of interest was reported by the author(s).