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Pulse-Seasonal Harvesting Via Nonlinear Delay Differential Equations and Applications in Fishery Management

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Abstract
  • We study the combined effects of periodically varying carrying capacity and survival rates on the fish population in the ocean (sea). We introduce a new delay differential equation model with a control parameter which describes how fish are harvested. We consider a predation function as the function of the delayed estimate of the true population. It is important to be able to model this delay because it has serious implications for the long term behavior of populations. We study the existence of global solutions for the initial value problem, extinction and persistence conditions, and the existence of periodic solutions. Along with qualitative studies we use numerical simulations to discuss some general models and the weekly tow-by-tow data for Pacific ocean perch (POP), obtained by the Pacific Biological Station (Nanaimo, BC) in 1995-2004.
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  • Idels, Lev V. and Beiyan Ou. 2006. Pulse-Seasonal Harvesting Via Nonlinear Delay Differential Equations and Applications in Fishery Management. In: Proceedings of the Thirteenth Biennial Conference of the International Institute of Fisheries Economics & Trade, July 11-14, 2006, Portsmouth, UK: Rebuilding Fisheries in an Uncertain Environment. Compiled by Ann L. Shriver. International Institute of Fisheries Economics & Trade, Corvallis, Oregon, USA, 2006. CD ROM. ISBN 0-9763432-3-1
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  • The National Oceanic & Atmospheric Administration Marine Fisheries Service, United States Department of Commerce (NOAA Fisheries); United Kingdom Department for Environment, Food and Rural Affairs (DEFRA); The United States Agency for International Development supported Aquaculture Collaborative Research and Support Program (ACRSP).
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