DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
A reaction-diffusion logistic population model with spatially nonhomogeneous harvesting is considered. It is shown that when the intrinsic growth rate is larger than the principal eigenvalue of the protection zone, then the population is always sustainable; while in the opposite case, there exists a maximum allowable catch to avoid the population extinction. The existence of steady state solutions is also studied for both cases. The existence of an optimal harvesting pattern is also shown, and theoretical results are complemented by some numerical simulations for one-dimensional domains.
Cui, Renhao; Li, Haomiao; Mei, Linfeng; and Shi, Junping, EFFECT OF HARVESTING QUOTA AND PROTECTION ZONE IN A REACTION-DIFFUSION MODEL ARISING FROM FISHERY MANAGEMENT (2017). DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 22(3).