Skip to main content
SpringerLink
Log in

Stability of attractivity regions for autonomous functional differential equations

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

Abstract

We consider attractivity regions of the zero solutions of autonomous retarded functional differential equations (FDEs). It is shown that the attractivity region remains unchanged if the FDE undergoes a small perturbation in certain classes of FDEs. Especially we obtain the openness of the set of parameters α∈(0,π/2) such that the attractivity region of the equation\(\dot x(t) = - \alpha x(t - 1)[1 + x(t)]\) is given by the set of continuous functions ϕ:[−1,0] → R with ϕ(0)>−1.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. DUNKEL, G.: “Single species model for population growth depending on past history” in: Seminar on differential equations and dynamical systems (Lecture notes in mathematics 60), 92–99, Berlin-Heidelberg-New York: Springer 1968.

    Google Scholar 

  2. HALE, J.K.: Functional differential equations, Berlin-Heidelberg-New York: Springer 1971.

    Google Scholar 

  3. HALE, J.K.: “Local behaviour of autonomous neutral functional differential equations” in: Ordinary differential equations, 95–107, New York: Academic Press 1972.

    Google Scholar 

  4. KAPLAN, J.L., YORKE, J.A.: On the stability of a periodic solution of a differential-delay equation. To appear.

  5. KAPLAN, J.L., YORKE, J.A.: Ordinary differential equations which yield periodic solutions of differentialdelay equations. J. Math. An. Appl.48, 317–325 (1974).

    Google Scholar 

  6. NUSSBAUM, R.D.: Periodic solutions of some nonlinear autonomous functional differential equations. To appear.

  7. NUSSBAUM, R.D.: A global bifurcation theorem with application to functional differential equations. To appear.

  8. WALTER, W.: Gewöhnliche Differentialgleichungen, Berlin-Heidelberg-New York: Springer 1972.

    Google Scholar 

  9. WALTHER, H.O.: Existence of a non-constant periodic solution of a nonlinear autonomous functional differential equation representing the growth of a single species population. Journal of Math. Biology1, 227–241 (1975).

    Google Scholar 

  10. WRIGHT, E.M.: A non-linear difference-differential equation. Jour. Reine Angew. Math.194, 66–87 (1955).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematisches Institut der Universität München, Theresienstr. 39, D-8000, München 2

    Hans-Otto Walther

Authors
  1. Hans-Otto Walther
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Walther, HO. Stability of attractivity regions for autonomous functional differential equations. Manuscripta Math 15, 349–363 (1975). https://doi.org/10.1007/BF01486605

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01486605

Keywords

Search

Navigation