Geodesic
Stability of one-parameter systems of linear autonomous differential equations with bounded delay
Vestnik rossijskih universitetov. Matematika, Tome 23 (2018) no. 123, pp. 488-502 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider a system of linear autonomous differential equations with bounded delay in the case when its characteristic function depends linearly on one scalar parameter. The application of the D-subdivision method to the problem of constructing the stability region for this equation was developed.
Keywords: delay differential equations, autonomous equations, asymptotic stability, D-subdivision method. 
@article{VTAMU_2018_23_123_a18,
     author = {M. V. Mulyukov},
     title = {Stability of one-parameter systems of linear autonomous differential equations with bounded delay},
     journal = {Vestnik rossijskih universitetov. Matematika},
     pages = {488--502},
     year = {2018},
     volume = {23},
     number = {123},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTAMU_2018_23_123_a18/}
}
TY  - JOUR
AU  - M. V. Mulyukov
TI  - Stability of one-parameter systems of linear autonomous differential equations with bounded delay
JO  - Vestnik rossijskih universitetov. Matematika
PY  - 2018
SP  - 488
EP  - 502
VL  - 23
IS  - 123
UR  - http://geodesic.mathdoc.fr/item/VTAMU_2018_23_123_a18/
LA  - ru
ID  - VTAMU_2018_23_123_a18
ER  - 
%0 Journal Article
%A M. V. Mulyukov
%T Stability of one-parameter systems of linear autonomous differential equations with bounded delay
%J Vestnik rossijskih universitetov. Matematika
%D 2018
%P 488-502
%V 23
%N 123
%U http://geodesic.mathdoc.fr/item/VTAMU_2018_23_123_a18/
%G ru
%F VTAMU_2018_23_123_a18
M. V. Mulyukov. Stability of one-parameter systems of linear autonomous differential equations with bounded delay. Vestnik rossijskih universitetov. Matematika, Tome 23 (2018) no. 123, pp. 488-502. http://geodesic.mathdoc.fr/item/VTAMU_2018_23_123_a18/

[1] N. V. Azbelev, V. P. Maksimov, L. F. Rakhmatullina, Introduction to the Theory of Functional-Differential Equations, Nauka Publ., Moscow, 1991, 280 pp. (In Russian) | MR

[2] N. V. Azbelev, P. M. Simonov, Stability of Solutions of the Equations with Ordinary Derivatives, Perm State University Publ., Perm, 2001, 230 pp. (In Russian)

[3] N. V. Azbelev, P. M. Simonov, “Stability of equations with delayed argument”, Russian Mathematics, 1997, no. 6, 3–16 (In Russian) | MR

[4] A. D. Myshkis, Linear Differential Equations with Delayed Argument, Nauka Publ., Moscow, 1972, 351 pp. (In Russian) | MR

[5] M. M. Postnikov, Stable Polynomials, Editorial URSS, Moscow, 2004, 176 pp. (In Russian)

[6] L. S. Pontryagin, “On zeros of some transcendental functions”, Izvestiya: Mathematics, 6:3 (1942), 115–134 (In Russian) | MR

[7] N. N. Meyman, N. G. Chebotarev, The Routh-Hurwitz problem for polynomials and entire functions, Trudy Mat. Inst. Steklov., 26, Acad. Sci. USSR, Moscow–Leningrad, 1949, 332 pp. (In Russian)

[8] A. V. Mikhaylov, “Method of harmonic analysis in control theory”, Automation and Remote Control, 1938, no. 3, 27–81 (In Russian)

[9] Yu. I. Neymark, Stability of Linearized Systems (Discrete and Distributed), Leningrad Holding the Order of the Red Banner Air Force Engineering Academy Publ., Leningrad, 1949, 140 pp. (In Russian)

[10] M. V. Mulyukov, “Structure of the D-subdivision domains for the two-parameter characteristic equations of systems with delay”, “Functional-Differential Equiations: Theory and Applications”, Proceedings of the Conference “Functional-Differential Equiations: Theory and Applications” Dedicated to the 95th Anniversary of Professor N.V. Azbelev (Perm, 2018), Proceedings of the Conference, 2018, 180–200 (In Russian)

[11] M. V. Mulyukov, “D-subdivision domains with straight bounds”, “Mathematics in the Modern World”, Proceedings of the All-Russian Conference “Mathematics in the Modern World” (Novosibirsk, 2017), Proceedings of the Conference, 2018, 233 (In Russian)

[12] M. V. Mulyukov, “Classification of Two-Parameter Autonomous Linear Systems with Delay”, Journal of Mathematical Sciences, 230:5 (2018), 724–727 | DOI | MR

[13] P. Lankaster, The Theory of Matrices, Academic Press, New York, 1969, 316 pp. | MR | MR

[14] A. I. Markushevich, Entire Functions. Elementary Essay, Nauka Publ., Moscow, 1975, 120 pp. (In Russian)

[15] V. A. Trenogin, Functional Analysis, Fizmatlit Publ., Moscow, 2007, 488 pp. (In Russian)

[16] G. Stepan, Retarded dynamical systems: stability and characteristic functions, John Wiley Sons, New York, 1989, 151 pp. | MR

[17] B. D. Hassard, N. D. Kazarinoff, T.-H. Wan, Theory and Applications of Hopf Bifurcation, Cambridge University Press, Cambridge, 1981, 280 pp. | MR

[18] M. Yu. Vagina, “A Delay-Averaged Logistic Model”, Automation and Remote Control, 2003, no. 4, 167–173 (In Russian) | MR