Classification of Two-Parameter Autonomous Linear Systems with Delay

Abstract

We carry out a classification of two-parameter linear autonomous differential systems with delay with respect to the type of boundaries of domains of a D-partition.

This is a preview of subscription content, access via your institution.

References

  1. 1.

    N. V. Azbelev, V. P. Maksimov, and L. F. Rakhmatullina, Introduction to the Theory of Linear Functional Differential Equations, World Federation Publ., Atlanta (1995).

  2. 2.

    E. N. Gryazina, “On the theory of D-partitions,” Avtomat. Telemekh., 12, 15–28 (2004).

    MathSciNet  MATH  Google Scholar 

  3. 3.

    A. D. Myshkis, Linear Differential Equations with Delayed Arguments [in Russian], Nauka, Moscow (1972).

    Google Scholar 

  4. 4.

    Yu. I. Neimark, “On the values of parameters for which a system of automatic regulation is stable,” Avtomat. Telemekh., 9, No. 3, 190–203 (1948).

    MathSciNet  Google Scholar 

  5. 5.

    Yu. I. Neimark, Dynamical Systems and Controllable Processes [in Russian], Nauka, Moscow (1978).

    Google Scholar 

  6. 6.

    V. A. Trenogin, Functional Analysis [in Russian], Nauka, Moscow (2007).

    Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to M. V. Mulyukov.

Additional information

Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 132, Proceedings of International Symposium “Differential Equations–2016,” Perm, 2016.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Mulyukov, M.V. Classification of Two-Parameter Autonomous Linear Systems with Delay. J Math Sci 230, 724–727 (2018). https://doi.org/10.1007/s10958-018-3777-1

Download citation

Keywords and phrases

  • system with delay
  • method of D-partition
  • asymptotic stability

AMS Subject Classification

  • 34K06
  • 34K20