Skip to main content

Nonvulnerability of Two Species Interactions

  • Conference paper
Renewable Resource Management

Part of the book series: Lecture Notes in Biomathematics ((LNBM,volume 40))

Abstract

The standard stability analysis of an ecosystem model assumes that the model is not disturbed after an initial perturbation. But ecosystems in the real world are subjected to frequent disturbances. The concept of nonvulnerability was developed to describe the ability of a dynamical system to remain healthy under continual disturbances.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Gilpin, M.E. and Ayala, F.J. 1973. Global Models of Growth and Competition Proc. Nat. Acad. Sci. USA, 70, 3590–3593

    Google Scholar 

  • Goh, B.S. 1975. Stability, Vulnerability and Persistence of Complex Ecosystems Ecological Modelling, 1, 105–116

    Google Scholar 

  • Goh, B.S. 1976. Nonvulnerability of Ecosystems in Unpredictable Environments Theor. Pop. Biol., 10, 83–95

    Google Scholar 

  • Goh, B.S. 1978. Global Stability in a Class of Prey-Predator Models Bull. Math. Biol., 40, 525–533

    Google Scholar 

  • Goh, B.S. 1979. Robust Stability Concepts For Ecosystem Models in Theoretical Systems Ecology (E. Halfon, Editor). Academic Press

    Google Scholar 

  • Grantham, W.J. and Vincent, T.L. 1975. A Controllability Maximum Principle JOTA, 17, 93–114

    Article  MathSciNet  MATH  Google Scholar 

  • Hahn, W. 1967. Stability of Motion Springer-Verlag, Berlin and New York.

    Google Scholar 

  • Harrison, G.W. 1979. Persistent Sets via Liapunov Functions Nonlinear Analysis, 3, 73–80

    Google Scholar 

  • LaSalle, J.P. and Lefschetz, S. 1961. Stability by. Liapunov’s Direct Method with Applications. Academic Press, New York

    Google Scholar 

  • Vincent, T.L. and Anderson, L.R. 1979. Return Time and Vulnerability for a Food Chain Model Theor. Pop. Biol., 15, 217–231

    Google Scholar 

  • Weiss, L. and Infante, E.F. 1967. Finite Time Stability under Perturbing Forces and on Product Spaces IEEE Trans. Automatic Control, 12, 54–59

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1981 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Fisher, M.E., Goh, B.S. (1981). Nonvulnerability of Two Species Interactions. In: Vincent, T.L., Skowronski, J.M. (eds) Renewable Resource Management. Lecture Notes in Biomathematics, vol 40. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46436-2_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-46436-2_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10566-4

  • Online ISBN: 978-3-642-46436-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics