Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 76, pp. 1-11.

Title: Bioeconomical Ricker's model of marine protected areas

Authors: Cameron N. Christou (Univ. of British Columbia, Vancouver, Canada)
         Lev V. Idels  (Univ. of British Columbia, Vancouver, Canada)

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.