Optimal control of integrodifference equations with growth-harvesting-dispersal order

Peng Zhong; Suzanne Lenhart

doi:10.3934/dcdsb.2012.17.2281

Article Contents

2012, Volume 17, Issue 6: 2281-2298. Doi: 10.3934/dcdsb.2012.17.2281

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Optimal control of integrodifference equations with growth-harvesting-dispersal order

Peng Zhong^1, and
Suzanne Lenhart^2,

1.
Department of Ecology, Evolution, and Natural Resources, Rutgers University, New Brunswick, NJ 08901
2.
Department of Mathematics, University of Tennessee, Knoxville, TN 37996-1300

Received: August 31, 2011

Revised: October 31, 2011

Published: August 2012

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Abstract

Integrodifference equations are discrete in time and continuous in space, and are used to model the spread of populations that are growing in discrete generations, or at discrete times, and dispersing spatially. We investigate optimal harvesting strategies, in order to maximize the profit and minimize the cost of harvesting. Theoretical results on the existence, uniqueness and characterization, as well as numerical results of optimized harvesting rates are obtained. The order of how the three events, growth, dispersal and harvesting, are arranged affects the harvesting behavior.

Keywords:

Integrodifference equations population model,
optimal control,
harvesting,
order of events.

Mathematics Subject Classification: Primary: 49J22, 92D25; Secondary: 39A05.

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