Electron. J. Diff. Equ., Vol. 2012 (2012), No. 76, pp. 1-11.

Bioeconomical Ricker's model of marine protected areas

Cameron N. Christou, Lev V. Idels

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.

Submitted November 29, 2011. Published May 14, 2012.
Math Subject Classifications: 34C60, 37N25, 49K15, 92B05.
Key Words: Marine protected areas; source-sink models; fishery models; bioeconomical analysis; Pontryagin's maximum principle; nonlinear differential equations.

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Cameron N. Christou
Department of Mathematics, University of British Columbia
Vancouver, B.C., V6T 1Z2, Canada
email: cnchrist@math.ubc.ca
Lev V. Idels
Department of Mathematics, Vancouver Island University
900 Fifth St. Nanaimo BC, V9S5S5, Canada
email: lev.idels@viu.ca

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