Multistability in a laser model with large delay
Modelirovanie i analiz informacionnyh sistem, Tome 17 (2010) no. 2, pp. 17-27.

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A dynamical model of laser generation based on monomode balance equations with delay is studied. Methods of a local analysis are used to build sets of quasinormal forms in the neighborhood of parameters bifurcation values. The possibility of the coexistence of a large number of steady oscillating states is shown.
Keywords: delay, normal form.
Mots-clés : singular perturbation
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E. V. Grigorieva; I. S. Kashchenko; S. A. Kashchenko. Multistability in a laser model with large delay. Modelirovanie i analiz informacionnyh sistem, Tome 17 (2010) no. 2, pp. 17-27. http://geodesic.mathdoc.fr/item/MAIS_2010_17_2_a1/

[1] S. Yanchuk, P. Perlikowski, “Delay and periodicity”, Phys. Rev. E, 79 (2009), 046221 | DOI | MR

[2] A. Loose, B. K. Goswami, H.-J. Wunsche, F. Henneberger, “Tristability of a semiconductor laser due to time-delayed optical feedback”, Phys. Rev. E, 79 (2009), 036211 | DOI

[3] T. Erneux, J. Grasman, “Limit-cycle oscillators subject to a delayed feedback”, Phys. Rev. E, 78 (2008), 026209 | DOI | MR

[4] E. V. Grigorieva, S. A. Kaschenko, N. A. Loiko, A. M. Samson, “Nonlinear dynamics in a laser with a negative delayed feedback”, Physica D, 59 (1992), 297–319 | DOI | Zbl

[5] E. V. Grigorieva, S. A. Kaschenko, “Regular and chaotic pulsations in lazer diode with delayed feedback”, Bifurcations and chaos, 6 (1993), 1515–1528 | DOI | Zbl

[6] H. Statz, G. A. De Mars, D. T. Wilson, C. L. Tang, “Problem of spike elimination in lasers”, J. Appl. Phys., 36 (1965), 1515–1516 | DOI

[7] S. A. Kaschenko, “Issledovanie metodami bolshogo parametra sistemy nelineinykh differentsialno-raznostnykh uravnenii, modeliruyuschikh zadachu khischnik-zhertva”, Dokl. AN SSSR, 266:4 (1982), 792–795 | MR

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

[9] S. A. Kaschenko, “Primenenie metoda normalizatsii k izucheniyu dinamiki differentsialno-raznostnykh uravnenii s malym mnozhitelem pri proizvodnoi”, Differentsialnye uravneniya, 25:8 (1989)

[10] M. Bestehorn, E. V. Grigorieva, H. Haken, S. A. Kaschenko, “Order parameters for class-B lasers with a long time delayed feedback”, Physica D, 145 (2000), 111–129 | MR

[11] S. A. Kaschenko, “O kvazinormalnykh formakh dlya parabolicheskikh uravnenii s maloi diffuziei”, DAN SSSR, 299:5 (1988), 1049–1052

[12] S. A. Kaschenko, “O korotkovolnovykh bifurkatsiyakh v sistemakh s maloi diffuziei”, Dokl. AN SSSR, 307:2 (1989), 269–273

[13] S. A. Kaschenko, “Uravneniya Ginzburga-Landau — normalnaya forma dlya differentsialno-raznostnogo uravneniya vtorogo poryadka s bolshim zapazdyvaniem”, Zhurnal vychisl. matem. i matem. fiz., 38:3 (1998), 457–465 | MR

[14] Novoe v sinergetike: vzglyad v trete tysyacheletie, Rossiiskaya akademiya nauk, eds. I. M. Makarov, G. G. Malinetskii, chlen-kor. RAN S. P. Kurdyumov, Nauka, M., 2002, 478 pp.

[15] I. S. Kaschenko, “Lokalnaya dinamika uravnenii s bolshim zapazdyvaniem”, Zhurnal Vychislitelnoi Matematiki i Matematicheskoi Fiziki, 48:12 (2008), 2141–2150 | MR

[16] M. Wolfrum, S. Yanchuk, “Eckhaus Instability in Systems with Large Delay”, Phys. Rev. Letters, 96 (2006), 220201 | DOI