Skip to main content

Optimal stationary exploitation of size-structured population with intra-specific competition

  • Chapter
Geometric Control Theory and Sub-Riemannian Geometry

Part of the book series: Springer INdAM Series ((SINDAMS,volume 5))

Abstract

We analyze an exploitation of size-structured population in stationary mode and prove the existence of stationary state of population for a given stationary control. The existence of an optimal control is proved and the necessary optimal condition is found.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Veliov V.M.: Optimal Control of Heterogeneous Systems: Basic Theory. J. Math. Anal. Appl. 346, 227–242 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  2. Hritonenko N., Yatsenko Yu., Goetz R., Xabadia A.: A bang-bang regime in optimal harvesting of size-structured populations. Nonlinear Analysis 71, e2331–e2336 (2009)

    Article  Google Scholar 

  3. Davydov A., Platov A.: Optimal Stationary Solution in Forest Management Model By Accounting Intra-Species Competition. MMJ 12(2), 269–273 (2012)

    MATH  MathSciNet  Google Scholar 

  4. Calsina A., Saldana J.: A model of physiologically structured population dynamics with nonlinear individual growth rate. J. Math. Biol. 33, 335–364 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  5. Kolmogorov A.N., Fomin S.V.: Elements of the Theory of Functions and Functional Analysis. Vol. 1: Metric and Normed Spaces. Courier Dover Publications, pp. 288 (1999)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Alexey A. Davydov .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Davydov, A.A., Platov, A.S. (2014). Optimal stationary exploitation of size-structured population with intra-specific competition. In: Stefani, G., Boscain, U., Gauthier, JP., Sarychev, A., Sigalotti, M. (eds) Geometric Control Theory and Sub-Riemannian Geometry. Springer INdAM Series, vol 5. Springer, Cham. https://doi.org/10.1007/978-3-319-02132-4_8

Download citation

Publish with us

Policies and ethics