Skip to main content

Logistic Models with Piecewise Arguments

  • Chapter
  • First Online:
  • 830 Accesses

Abstract

Differential equation with piecewise continuous argument (or DEPCA) will be discussed in this chapter.

There is no philosophy, which is not founded upon knowledge of the phenomena, but to get any profit from this knowledge it is absolutely necessary to be a mathematician.

Daniel Bernoulli (1700–1782).

When a mathematician has no more ideas he pursues axiomatics.

Felix Klein (1849–1925).

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
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

Learn about institutional subscriptions

References

  1. H.I. Freedman, H. Xia, Periodic solutions of single species models with delay, differential equations, dynamical systems and control science. Lect. Notes Pure Appl. Math. 152, 55–74 (1994)

    MathSciNet  Google Scholar 

  2. R.E. Gaines, J.L. Mawhin, Coincidence Degree and Nonlinear Differential Equations (Springer, Berlin, 1977)

    MATH  Google Scholar 

  3. G. Li, Oscillatory behavior of solutions to a generalized, nonautonomous, delay logistic equation. Ann. Differ. Equat. 7, 432–438 (1991)

    MATH  Google Scholar 

  4. P. Liu, K. Gopalsamy, Global stability and chaos in a population model with piecewise constant arguments. Appl. Math. Comput. 101, 63–88 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  5. X. Liu, A. Wilmas, Impulsivev stabilizability of autonoumous systems. J. Math. Anal. Appl. 44, 171–182 (1992)

    MATH  Google Scholar 

  6. J. Luo, Oscillation and linearized oscillation of logistic equation with several delays. Appl. Math. Comput. 131, 469–476 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  7. T.R. Malthus, An Essay on the Principle of Population (Johnson, London, 1798)

    Google Scholar 

  8. J.H. Shen, J.S. Yu, Nonlinear delay differential equations with impulsive perturbations. Math. Appl. 9(3), 272–277 (1996)

    MATH  MathSciNet  Google Scholar 

  9. X.H. Tang, Oscillation for first order nonlinear delay differential equations. J. Math. Anal. Appl. 292, 211–221 (2004)

    Article  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). Logistic Models with Piecewise Arguments. In: Oscillation and Stability of Delay Models in Biology. Springer, Cham. https://doi.org/10.1007/978-3-319-06557-1_4

Download citation

Publish with us

Policies and ethics