Geodesic
Local dynamics of the model of a semiconductor laser with delay
Teoretičeskaâ i matematičeskaâ fizika, Tome 215 (2023) no. 2, pp. 232-241 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We study a model of a semiconductor laser with delay. We discuss the stability of the equilibrium and single out bifurcation parameter values. It turns out that resultant critical cases have infinite dimensions. In the cases where the parameter values are close to critical ones, we constructed first-approximation equations for the asymptotic expansions of solution amplitudes. These equations are nonlinear boundary-value problems of parabolic type, containing integral terms in the nonlinearity in some cases. We present asymptotic formulas that relate solutions of the original model to the constructed boundary-value problems.
Keywords: delay, laser model, dynamics, asymptotics. 
@article{TMF_2023_215_2_a5,
     author = {I. S. Kashchenko and S. A. Kaschenko},
     title = {Local dynamics of the~model of a~semiconductor laser with delay},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {232--241},
     year = {2023},
     volume = {215},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2023_215_2_a5/}
}
TY  - JOUR
AU  - I. S. Kashchenko
AU  - S. A. Kaschenko
TI  - Local dynamics of the model of a semiconductor laser with delay
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2023
SP  - 232
EP  - 241
VL  - 215
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2023_215_2_a5/
LA  - ru
ID  - TMF_2023_215_2_a5
ER  - 
%0 Journal Article
%A I. S. Kashchenko
%A S. A. Kaschenko
%T Local dynamics of the model of a semiconductor laser with delay
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2023
%P 232-241
%V 215
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2023_215_2_a5/
%G ru
%F TMF_2023_215_2_a5
I. S. Kashchenko; S. A. Kaschenko. Local dynamics of the model of a semiconductor laser with delay. Teoretičeskaâ i matematičeskaâ fizika, Tome 215 (2023) no. 2, pp. 232-241. http://geodesic.mathdoc.fr/item/TMF_2023_215_2_a5/

[1] A. G. Vladimirov, D. Turaev, “Model for passive mode locking in semiconductor lasers”, Phys. Rev. A, 72:3 (2005), 033808, 13 pp. | DOI

[2] A. Pimenov, J. Javaloyes, S. V. Gurevich, A. G. Vladimirov, “Light bullets in a time-delay model of a wide-aperture mode-locked semiconductor laser”, Philos. Trans. Roy. Soc. A, 376:2124 (2018), 20170372, 14 pp. | DOI | MR

[3] A. G. Vladimirov, D. Rachinskii, M. Wolfrum, “Modeling of passively mode-locked semiconductor lasers”, Nonlinear Laser Dynamics: From Quantum Dots to Cryptography, Wiley-VCH, New York, 2012 | DOI

[4] M. Nizette, D. Rachinskii, A. G. Vladimirov, M. Wolfrum, “Pulse interaction via gain and loss dynamics in passive mode locking”, Phys. D, 218:1 (2006), 95–104 | DOI

[5] M. Bestehorn, E. V. Grigorieva, H. Haken, S. A. Kaschenko, “Order parameters for class-B lasers with a long time delayed feedback”, Phys. D, 145:1–2 (2000), 110–129 | DOI | MR

[6] S. Yanchuk, G. Giacomelli, “Spatio-temporal phenomena in complex systems with time delays”, J. Phys. A: Math. Theor., 50:10 (2017), 103001, 56 pp. | DOI | MR

[7] S. A. Kaschenko, “Primenenie metoda normalizatsii k izucheniyu dinamiki differentsialno-raznostnogo uravneniya s malym mnozhitelem pri proizvodnoi”, Differents. uravneniya, 25:8 (1989), 1448–1451 | MR | Zbl

[8] I. S. Kaschenko, “Lokalnaya dinamika uravnenii s bolshim zapazdyvaniem”, Zh. vychisl. matem. i matem. fiz., 48:12 (2008), 2141–2150 | DOI | MR

[9] A. V. Gaponov-Grekhov, M. I. Rabinovich, “Uravnenie Ginzburga–Landau i nelineinaya dinamika neravnovesnykh sred”, Izv. vuzov. Radiofizika, 30:2 (1987), 131–143 | DOI

[10] T. S. Akhromeeva, S. P. Kurdyumov, G. G. Malinetskii, A. A. Samarskii, Nestatsionarnye struktury i diffuzionnyi khaos, Nauka, M., 1992 | MR

[11] A. Yu. Loskutov, A. S. Mikhailov, Osnovy teorii slozhnykh sistem, In-t kompyuternykh issledovanii, M.–Izhevsk, 2007