Skip to main content

Stability of Delay Logistic Models

  • Chapter
  • First Online:
Oscillation and Stability of Delay Models in Biology

Abstract

The stability of the equilibrium points is important in the study of mathematical models. The equilibrium point \(\overline{N}\) is locally stable if the solution of the model N(t) approaches \(\overline{N}\) as time increases for all the initial values, in some neighborhood of \(\overline{N}\).

The essence of mathematics lies in its freedom.

Georg Cantor (1845–1915).

As for everything else, so for a mathematical theory: beauty can be perceived but not explained.

Arthur Cayley (1821–1895).

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. M.P. Chen, J.S. Yu, X.Z. Qian, Z.C. Wang, On the stability of a delay differential population model. Nonlinear Anal. Theor. Meth. Appl. 25, 187–195 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  2. H.I. Freedman, J.W.-H. So, Global stability and persistence of simple food chain. Math. Biosci. 76, 69–86 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  3. M.B. Schaefer, Some aspects of the dynamics of populations important to the management of commercial marine fisheries. Bull. Inter-American Tropical Tuna Commission 1, 25–26 (1954)

    Google Scholar 

  4. G.A. Shanholt, A nonlinear variation of constant formula for functional differential equations. Math. Syst. Theor. 6, 343–352 (1972/1973)

    Google Scholar 

  5. F.E. Smith, Population dynamics in daphnia magna and a new model for population growth. Ecology 44, 651–663 (1963)

    Article  Google Scholar 

  6. M.E. Turner, B.A. Blumenstein, J.L. Sebaugh, A generalization of the logistic law of growth. Biometrics 25, 577–580 (1969)

    Article  Google Scholar 

  7. E.M. Wright, A nonlinear difference-differential equations. J. Reine Angew. Math. 494, 66–87 (1955)

    Google Scholar 

  8. J. Yan, A. Zhao, Oscillation and stability of linear impulsive delay differential equations. J. Math. Anal. Appl. 227, 187–194 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  9. J.S. Yu, Global attractivity of the zero solution of a class of functional differential equations and its applications. Sci. China Ser. A 39, 225–237 (1996)

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Agarwal, R.P., O’Regan, D., Saker, S.H. (2014). Stability of Delay Logistic Models. In: Oscillation and Stability of Delay Models in Biology. Springer, Cham. https://doi.org/10.1007/978-3-319-06557-1_3

Download citation

Publish with us

Policies and ethics