Bioeconomical Ricker's model of marine protected areas

Marine protected areas (MPA) become part of modern fishery management to safeguard marine life and sustain ecosystem processes. Based on a classical Ricker's model, the deterministic nonlinear sink-source model of MPA is presented. Sufficient conditions for the existence of positive bounded ste...

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Bibliographic Details
Published inElectronic journal of differential equations Vol. 2012; no. 76; pp. 1 - 11
Main Authors Cameron N. Christou, Lev V. Idels
Format Journal Article
LanguageEnglish
Published Texas State University 14.05.2012
Subjects
bioeconomical analysis
fishery models
Marine protected areas
nonlinear differential equations
Pontryagin's maximum principle
source-sink models
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Summary:Marine protected areas (MPA) become part of modern fishery management to safeguard marine life and sustain ecosystem processes. Based on a classical Ricker's model, the deterministic nonlinear sink-source model of MPA is presented. Sufficient conditions for the existence of positive bounded steady-states are obtained. The present value of net revenue is maximized subject to population dynamics in the fishing zone and in the protected area. The analysis has shown that there is an optimal equilibrium solution, and the best harvesting policy to attain this equilibrium position is a bang-bang control effort. It was demonstrated numerically by comparing the optimal harvesting rate against a constant harvesting rate, and the fast convergence to the optimal equilibrium guarantees greater profits under the optimal harvesting strategy.
ISSN:1072-6691