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Sustainable Harvesting Policies Under Long-Run Average Criteria: Near Optimality

Sustainable Harvesting Policies Under Long-Run Average Criteria: Near Optimality This paper develops near-optimal sustainable harvesting strategies for the predator in a predator-prey system. The objective function is of long-run average per unit time type in the path-wise sense. To date, ecological systems under environmental noise are usually modeled as stochastic differential equations driven by a Brownian motion. Recognizing that the formulation using a Brownian motion is only an idealization, in this paper, it is assumed that the environment is subject to disturbances characterized by a jump process with rapid jump rates. Under broad conditions, it is shown that the systems under consideration can be approximated by a controlled diffusion system. Based on the limit diffusion system, control policies of the original systems are constructed. Such an approach enables us to develop sustainable harvesting policies leading to near optimality. To treat the underlying problems, one of the main difficulties is due to the long-run average objective function. This in turn, requires the handling of a number of issues related to ergodicity. New approaches are developed to obtain the tightness of the underlying processes based on the population dynamic systems. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Sustainable Harvesting Policies Under Long-Run Average Criteria: Near Optimality

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Publisher
Springer Journals
Copyright
Copyright © Springer Science+Business Media, LLC, part of Springer Nature 2018
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
ISSN
0095-4616
eISSN
1432-0606
DOI
10.1007/s00245-018-9504-y
Publisher site
See Article on Publisher Site

Abstract

This paper develops near-optimal sustainable harvesting strategies for the predator in a predator-prey system. The objective function is of long-run average per unit time type in the path-wise sense. To date, ecological systems under environmental noise are usually modeled as stochastic differential equations driven by a Brownian motion. Recognizing that the formulation using a Brownian motion is only an idealization, in this paper, it is assumed that the environment is subject to disturbances characterized by a jump process with rapid jump rates. Under broad conditions, it is shown that the systems under consideration can be approximated by a controlled diffusion system. Based on the limit diffusion system, control policies of the original systems are constructed. Such an approach enables us to develop sustainable harvesting policies leading to near optimality. To treat the underlying problems, one of the main difficulties is due to the long-run average objective function. This in turn, requires the handling of a number of issues related to ergodicity. New approaches are developed to obtain the tightness of the underlying processes based on the population dynamic systems.

Journal

Applied Mathematics and Optimization – Springer Journals

Published: Apr 28, 2020

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