Skip to main content
SpringerLink
Log in

Averaging principles applied to logistic equations with rapidly oscillating delays

  • Published:
Automatic Control and Computer Sciences Aims and scope Submit manuscript

Abstract

The problem about local dynamics of the logistic equation with a rapidly oscillating timeperiodic piecewise constant coefficient of delay has been considered. It has been shown that the averaged equation is a logistic equation with two delays. A stability criterion for equilibrium points has been obtained. The dynamical properties of the original equation are considered provided that the critical case of the equilibrium point stability problem has been implemented. It has been found that an increase of delay coefficient oscillation frequency may lead to an unlimited process of steady-mode birth and death.

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. Wu, J., Theory and Applications of Partial Functional Differential Equations, Springer-Verlag, 1996.

    Book  MATH  Google Scholar 

  2. Bogoliubov, N.N. and Mitropolsky, Y.A., Asymptotic Methods in the Theory of Non-Linear Oscillations, New York: Gordon and Breach, 1961.

    Google Scholar 

  3. Kolesov, Yu.S., Kolesov, V.S., and Fedik, I.I., Avtokolebaniya v sistemakh s raspredelennymi parametrami (Self-Oscillations in Systems with Distributed Parameters), Naukova Dumka, 1979.

    Google Scholar 

  4. Kolesov, Yu.S. and Mayorov, V.V., A new method for studying the stability of solutions of linear differential equations with constant close to almost periodic coefficients, Differ. Uravn., 1974, no. 10, pp. 1778–1788.

    Google Scholar 

  5. Glyzin, S.D., Accounting of age groups in the Hutchinson equation, Model. Anal. Inf. Syst., 2007, vol. 14, no. 3, pp 29–42.

    MathSciNet  Google Scholar 

  6. Kashchenko, S.A. and Mayorov, V.V., An algorithm for studying the stability of solutions of linear differential equations with aftereffect and rapidly oscillating coefficients, Issledovaniya po ustoichivosti i teorii kolebanii (Studies of Stability and the Theory of Oscillations), Yaroslavl, 1977, pp. 70–81.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. National Research Nuclear University MEPhI, sh. Kashirskoe 31, Moscow, 115409, Russia

    N. D. Bykova

  2. Demidov Yaroslavl State University, sh. Sovetskaya 14, Yaroslavl, 150000, Russia

    N. D. Bykova

  3. Belarus State Economical University, pr. Partizanskii 26, Minsk, 220070, Belarus

    E. V. Grigorieva

Authors
  1. N. D. Bykova
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. V. Grigorieva
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to N. D. Bykova.

Additional information

Original Russian Text © N.D. Bykova, E.V. Grigorieva, 2014, published in Modelirovanie i Analiz Informatsionnykh Sistem, 2014, Vol. 21, No. 1, pp. 89–93.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bykova, N.D., Grigorieva, E.V. Averaging principles applied to logistic equations with rapidly oscillating delays. Aut. Control Comp. Sci. 50, 567–570 (2016). https://doi.org/10.3103/S0146411616070026

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S0146411616070026

Keywords

Search

Navigation