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

Sustainable Harvesting Policies Under Long-Run Average Criteria: Near Optimality Appl Math Optim https://doi.org/10.1007/s00245-018-9504-y Sustainable Harvesting Policies Under Long-Run Average Criteria: Near Optimality 1 2 Dang H. Nguyen · George Yin © Springer Science+Business Media, LLC, part of Springer Nature 2018 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 ide- alization, 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 har- vesting 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 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

Nguyen, Dang; Yin, George
Applied Mathematics and Optimization, Volume OnlineFirst – May 28, 2018
36 pages
Read Article

Loading next page...
 
/lp/springer_journal/sustainable-harvesting-policies-under-long-run-average-criteria-near-pRMKuOdn2z
Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer Science+Business Media, LLC, part of Springer Nature
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

Appl Math Optim https://doi.org/10.1007/s00245-018-9504-y Sustainable Harvesting Policies Under Long-Run Average Criteria: Near Optimality 1 2 Dang H. Nguyen · George Yin © Springer Science+Business Media, LLC, part of Springer Nature 2018 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 ide- alization, 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 har- vesting 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

Journal

Applied Mathematics and Optimization – Springer Journals

Published: May 28, 2018

References

  • Singular stochastic control in the presence of a state-dependent yield structure
    Alvarez, LHR
  • Optimal multi-dimensional stochastic harvesting with density-dependent prices
    Alvarez, LHR; Lungu, E; Øksendal, B
  • Bioeconomics of Fisheries Management
    Anderson, LG; Seijo, JC
  • Ergodic Control of Diffusion Processes
    Arapostathis, A; Borkar, VS; Ghosh, MK
  • Stability analysis of harvesting in a predator-prey model
    Azar, C; Holmberg, J; Lindgren, K
  • Harvesting from a prey-predator complex
    Beddington, JR; Cooke, JG
  • Lotka Volterra in fluctuating environment or “how switching between beneficial environments can make survival harder”
    Benaïm, M; Lobry, C
  • Stability and control of stochastic systems with wide-band noise disturbances. I
    Blankenship, G; Papanicolaou, GC
  • Mathematical Bioeconomics: The Mathematics of Conservation
    Clark, CW
  • Predator harvesting in stage dependent predation models: insights from a threshold management policy
    Silveira Costa, MI
  • Asymptotic behavior of Kolmogorov systems with predator-prey type in random environment
    Du, NH; Nguyen, DH
  • Conditions for permanence and ergodicity of certain stochastic predator-prey models
    Du, NH; Nguyen, DH; Yin, G
  • Deterministic and Stochastic Optimal Control
    Fleming, WH; Rishel, R
  • Stochastic population growth in spatially heterogeneous environments: the density-dependent case
    Hening, A; Nguyen, D; Yin, G
  • Nearly optimal state feedback controls for stochastic systems with wideband noise disturbances
    Kushner, HJ; Runggaldier, W
  • Optimal harvesting policy for a stochastic predator-prey model
    Liu, M; Bai, C
  • Analysis of a stochastic tri-trophic food-chain model with harvesting
    Liu, M; Bai, C
  • Optimal harvesting from interacting populations in a stochastic environment
    Lungu, EM; Øksendal, B
  • Stochastic population dynamics under regime switching. II
    Luo, Q; Mao, X
  • Conservation of Biological Resources
    Milner-Gulland, EJ; Mace, R
  • Coexistence and exclusion of stochastic competitive Lotka-Volterra models
    Nguyen, DH; Yin, G
  • Long-time behaviour of a stochastic prey-predator model
    Rudnicki, R
  • Persistence in fluctuating environments
    Schreiber, SJ; Benaïm, M; Atchade, KAS
  • Asymptotic Methods in the Theory of Stochastic Differential Equations
    Skorokhod, AV
  • On optimal harvesting problems in random environments
    Song, Q; Stockbridge, RH; Zhu, C
  • Optimal harvesting strategies for stochastic competitive Lotka-Volterra ecosystems
    Tran, K; Yin, G
  • Dynamics in a ratio-dependent predator-prey model with predator harvesting
    Xiao, DM; Li, WX; Han, MA
  • On strong Feller, recurrence, and weak stabilization of regime-switching diffusions
    Zhu, C; Yin, G

You’re reading a free preview. Subscribe to read the entire article.

Try 2 weeks free now

DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

or browse the journals available

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create folders to
organize your research

Export folders, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off

Sign up
for free
Start 14 day
Free Trial