Skip to main content
Log in

On exponential stability of solutions to periodic neutral-type systems

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

Abstract

We consider periodic systems of delay equations. Exponential stability conditions for the zero solution are pointed out by using the Lyapunov-Krasovskiĭ functional. We give some estimates that characterize the decay rate of solutions at infinity.

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

Access this article

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. El’sgol’ts L. E. and Norkin S. B., Introduction to the Theory and Application of Differential Equations with Deviating Arguments, Academic Press, New York and London 1973).

    MATH  Google Scholar 

  2. Hale J. K., Theory of Functional Differential Equations, Springer-Verlag, New York, Heidelberg, and Berlin 1977).

    Book  MATH  Google Scholar 

  3. Korenevskiĭ D. G., Stability of Dynamical Systems Under Random Perturbations of Their Parameters. Algebraic Criteria [Russian], Naukova Dumka, Kiev 1989).

    Google Scholar 

  4. Azbelev N. V., Maksimov V. P., and Rakhmatullina L. F., Introduction to the Theory of Functional-Differential Equations [Russian], Nauka, Moscow 1991).

    MATH  Google Scholar 

  5. Dolgiĭ Yu. F., Stability of Periodic Differential-Difference Equations [Russian], Izdat. Ural Univ., Ekaterinburg 1996).

    Google Scholar 

  6. Kolmanovskii V. B. and Myshkis A. D., Introduction to the Theory and Applications of Functional-Differential Equations, Kluwer Acad. Publ., Dordrecht 1999) (Math. Appl.; vol. 463).

    Book  MATH  Google Scholar 

  7. Gu K., Kharitonov V. L., and Chen J., Stability of Time-Delay Systems, Birkhäuser, Boston 2003).

    Book  MATH  Google Scholar 

  8. Agarwal R. P., Berezansky L., Braverman E., and Domoshnitsky A., Nonoscillation Theory of Functional Differential Equations with Applications, Springer-Verlag, New York 2012).

    Book  MATH  Google Scholar 

  9. Gil’ M. I., Stability of Neutral Functional Differential Equations, Atlantis Press, Paris 2014) (Atlantis Stud. Differ. Equ.; vol. 3).

    Book  MATH  Google Scholar 

  10. MacDonald N., Biological Delay Systems: Linear Stability Theory, Camb. Univ. Press, Cambridge 1989) (Camb. Stud. Math. Biol.; vol. 8).

    MATH  Google Scholar 

  11. Kuang Y., Delay Differential Equations with Applications in Population Dynamics, Acad. Press, Boston 1993) (Math. Sci. Eng.; vol. 191).

    MATH  Google Scholar 

  12. Erneux T., Applied Delay Differential Equations, Springer-Verlag, New York 2009) (Surv. Tutorials Appl. Math. Sci.; vol. 3).

    MATH  Google Scholar 

  13. Demidenko G. V. and Matveeva I. I., “Stability of solutions to delay differential equations with periodic coefficients of linear terms,” Sib. Math. J., vol. 48, no. 5, 824–836 (2007).

    Article  MATH  Google Scholar 

  14. Matveeva I. I., “Estimates of solutions to a class of systems of nonlinear delay differential equations,” J. Appl. Ind. Math., vol. 7, no. 4, 557–566 (2013).

    Article  MathSciNet  MATH  Google Scholar 

  15. Demidenko G. V. and Matveeva I. I., “On estimates of solutions to systems of differential equations of neutral type with periodic coefficients,” Sib. Math. J., vol. 55, no. 5, 866–881 (2014).

    Article  MathSciNet  MATH  Google Scholar 

  16. Demidenko G. V. and Matveeva I. I., “Estimates for solutions to a class of time-delay systems of neutral type with periodic coefficients and several delays,” Electron. J. Qual. Theory Differ. Equ., vol. 2015, no. 83, 1–22 (2015).

    Article  MathSciNet  MATH  Google Scholar 

  17. Demidenko G. V. and Matveeva I. I., “On stability of solutions to linear systems with periodic coefficients,” Sib. Math. J., vol. 42, no. 2, 282–296 (2001).

    Article  MathSciNet  MATH  Google Scholar 

  18. Daleckiĭ Ju. L. and Kreĭn M. G., Stability of Solutions to Differential Equations in Banach Space, Amer. Math. Soc., Providence 1974).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to I. I. Matveeva.

Additional information

The author was supported by the Russian Foundation for Basic Research (Grant 16–01–00592).

Novosibirsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 58, No. 2, pp. 344–352, March–April, 2017; DOI: 10.17377/smzh.2017.58.208.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Matveeva, I.I. On exponential stability of solutions to periodic neutral-type systems. Sib Math J 58, 264–270 (2017). https://doi.org/10.1134/S0037446617020082

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0037446617020082

Keywords

Navigation