Geodesic
On the location of some characteristic quasipolinomial roots
Modelirovanie i analiz informacionnyh sistem, Tome 22 (2015) no. 1, pp. 74-84 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The location of zeros of two characteristic quasi-polynomials arising from studying the differential equations with a retarded argument is considired. The first one originates from the mathematical model of electromagnetic oscillations generator with a delayed feedback, the second one — from the Lang–Kobayashi system that is a well-known mathematical model of a quantum generator. The D-partition figures are presented in a prameter space and possible critical cases are found out. The large delay case important for applications is considered. In this case, for quasi-polinomial roots obtained are the analytical dependencies on a value reciprocal to the delay, and uniform asymptotical formulas are constructed.
Mots-clés : quasi-polynomial
Keywords: D-partition method, asymptotic representation. 
@article{MAIS_2015_22_1_a4,
     author = {D. S. Glyzin and E. P. Kubyshkin and A. R. Moryakova},
     title = {On the location of some characteristic quasipolinomial roots},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {74--84},
     year = {2015},
     volume = {22},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2015_22_1_a4/}
}
TY  - JOUR
AU  - D. S. Glyzin
AU  - E. P. Kubyshkin
AU  - A. R. Moryakova
TI  - On the location of some characteristic quasipolinomial roots
JO  - Modelirovanie i analiz informacionnyh sistem
PY  - 2015
SP  - 74
EP  - 84
VL  - 22
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/MAIS_2015_22_1_a4/
LA  - ru
ID  - MAIS_2015_22_1_a4
ER  - 
%0 Journal Article
%A D. S. Glyzin
%A E. P. Kubyshkin
%A A. R. Moryakova
%T On the location of some characteristic quasipolinomial roots
%J Modelirovanie i analiz informacionnyh sistem
%D 2015
%P 74-84
%V 22
%N 1
%U http://geodesic.mathdoc.fr/item/MAIS_2015_22_1_a4/
%G ru
%F MAIS_2015_22_1_a4
D. S. Glyzin; E. P. Kubyshkin; A. R. Moryakova. On the location of some characteristic quasipolinomial roots. Modelirovanie i analiz informacionnyh sistem, Tome 22 (2015) no. 1, pp. 74-84. http://geodesic.mathdoc.fr/item/MAIS_2015_22_1_a4/

[1] Neymark Yu. I., “Struktura D-razbienia prostranstva quasipolinomov diagrammi Vishnegradskogo i Nyquista”, Doklady AN SSSR, 60 (1948), 1503–1506 (in Russian)

[2] A. G. Sveshnikov, A. N. Tikhonov, The Theory of Functions of a Complex Variable, Translated from Russian by G. Yankovsky, Mir Publ., M., 1974

[3] R. Lang, Kobayashi, “Abundance of strange attractors”, IEEE. J. Quantum Electron, 16:1 (1980), 347–355 | DOI

[4] E. V. Grigorieva, H. Haken, S. A. Kaschenko, “Theory of quasi-periodicity in model of lasers with delayed optoelectronic feedback”, Optics Communications, 165 (1999), 279–292 | DOI

[5] E. V. Grigorieva, M. Bestehorn, H. Haken, S. A. Kaschenko, “Order parameters for class-B lasers with a long time delayed feedback”, Physica D, 145 (2000), 111–130

[6] Grigorieva E. V., Kaschenko I. S., Kaschenko S. A., “Multistability in a laser model with large delay”, Modeling and Analysis of Information Systems, 17:2 (2010), 17–27 (in Russian)

[7] R. Bellman, K. L. Cooke, Differential-Difference Equations, Academic Press, New York–London, 1963