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Differential movement and movement bias models for marine protected areas. (English) Zbl 1262.34049
In connection with marine protected areas for overfished stocks, the authors consider mathematical models constructed by means of boundary value problems for partial (and for describing the steady state – ordinary) differential equations. In the first of the considered models, the parameters are piecewise constant with the diffusion coefficient and mortality rate different inside and outside the protected area. Next, a movement bias model is studied. It is supposed here that at the boundary, the probability of moving to the protected area is higher than of moving outside. Finally, a model with constant diffusion coefficient and smooth in the space variable mortality rate is considered. Different models are analyzed and compared with empirical evidence.

MSC:
34C60 Qualitative investigation and simulation of ordinary differential equation models
34B60 Applications of boundary value problems involving ordinary differential equations
35Q92 PDEs in connection with biology, chemistry and other natural sciences
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