Cameron N. Christou, Lev V. Idels
Abstract:
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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