Abstract
We establish exact efficient asymptotic stability criteria for two-parameter systems of two autonomous delay differential equations.
This is a preview of subscription content, access via your institution.
References
- 1.
Mulyukov, M.V. “Separation of Equations in Certain Systems,” Vestn. TGU 18(16), 2617–2618 (2013).
- 2.
Mulyukov, M.V. “On Factorization of the Characteristic Quasipolynomial of a System of Linear Differential Equations with Delay,” Russian Mathematics (Iz. VUZ) 57, No. 9, 31–36 (2013).
- 3.
Hale, J. Theory of Functional Differential Equations (Springer Verlag, Gmbh, 1977; Mir, Moscow, 1984).
- 4.
Azbelev, N.V., Maksimov, V.P., and Rakhmatullina, L.F. Introduction to the Theory of Functional Differential Equations: Methods and Applications (Nauka, Moscow, 1991) [in Russian].
- 5.
Azbelev, N.V. and Simonov, P.M. Stability of Solutions to Ordinary Differential Equations (Permsk. Univ., Perm, 2001) [in Russian].
- 6.
Azbelev, N.V. and Simonov, P.M. “Stability of the Equations with Delay,” Russian Mathematics (Iz. VUZ) 41, No. 6, 1–14 (1997).
- 7.
Bellman, R. and Cooke, K.L. Differential-Difference Equations (Acad. Press, New York-London, 1963, Mir, Moscow, 1967).
- 8.
Andronov, A.A. and Maier, A.T. “The Simplest Linear Systems with Retardation,” Avtomatika i Telemekhanika, 7, Nos. 2, 3, 95–106 (1946).
- 9.
Postnikov, M.M. Stable Polynomials, 2nd Ed. (Editorial URSS, Moscow, 2004) [in Russian].
- 10.
Bykova, A.N. “The Study of Stability of Systems of Two Nonlinear Differential Equations with a Retarded Argument in the First Approximation,” Candidate’s Dissertation in Mathematics and Physics (Cheboksary, 2002).
- 11.
Elsgol’ts L.E. and Norkin, S.B. Introduction to the Theory of Differential Equations with Deviating Arguments (Nauka, Moscow, 1971) [in Russian].
- 12.
Hsu, C.S. and Bhatt, S.J. “Stability Charts for Second-Order Dynamical Systems with Time Lag,” J. Appl. Mech. 33(1), 119–124 (1966).
Author information
Affiliations
Corresponding author
Additional information
Original Russian Text © M.V. Mulyukov, 2014, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2014, No. 6, pp. 48–55.
About this article
Cite this article
Mulyukov, M.V. Asymptotic stability of two-parameter systems of delay differential equations. Russ Math. 58, 44–50 (2014). https://doi.org/10.3103/S1066369X1406005X
Received:
Published:
Issue Date:
Keywords
- delay equations
- asymptotic stability
- efficient criteria