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Influence of prey reserve in a prey–predator fishery. (English) Zbl 1108.34043
This is a detailed expository contribution to sustainable marine resources, featuring the promotion of marine reserves as a fisheries management tool. The authors discuss the formal connections between a prey-predator system in a two-patch environment, in which the prey migrate randomly between patches, but the predator (fishing) is not permitted in the reserved zone (prey refuge). Local and global stability of the system are analyzed and it is observed that in the presence of predators, the fish population may still be sustained at an appropriate equilibrium level if the population in the unreserved area lies in a certain interval. The optimal harvesting policy is also discussed using Pontryagin’s maximum principle, which helps to conclude that a high interest rate will cause a high inflation rate.

MSC:
34C60 Qualitative investigation and simulation of ordinary differential equation models
92D25 Population dynamics (general)
34D20 Stability of solutions to ordinary differential equations
34D05 Asymptotic properties of solutions to ordinary differential equations
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