Abstract
Dynamics of laser generation is considered on the base of single-mode rate equations with retarded argument. In the framework of local analysis, we determine continual sets of families of quasi-normal forms in the vicinity of the bifurcation parameter values. Their solutions imply the coexistence of a large number of steady oscillatory modes due to a large delay.
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Yanchuk, S. and Perlikowski, P., Delay and periodicity, Phys. Rev. E: Stat., Nonlin., and Soft Matter Phys., 2009, vol. 79, p. 046221.
Loose, A., Goswami, B.K., Wunsche, H.-J., and Henneberger, F., Tristability of a semiconductor laser due to time-delayed optical feedback, Phys. Rev. E: Stat., Nonlin., and Soft Matter Phys., 2009, vol. 79, p. 036211.
Erneux, T. and Grasman, J., Limit-cycle oscillators subject to a delayed feedback. Phys. Rev. E: Stat., Nonlin., and Soft Matter Phys., 2008, vol. 78, p. 026209.
Grigorieva, E.V., Kashchenko, S.A., Loiko, N.A., and Samson, A.M., Nonlinear dynamics in a laser with a negative delayed feedback, Physica D, 1992, vol. 59, pp. 297–319.
Grigorieva, E.V. and Kaschenko, S.A., Regular and chaotic pulsations in lazer diode with delayed feedback, Bifurcations and Chaos, 1993, vol. 6, pp. 1515–1528.
Statz, H., de Mars, G.A., Wilson, D.T., and Tang, C.L., Problem of spike elimination in lasers, J.Appl. Phys., 1965, vol. 36, pp. 1515–1516.
Kaschenko, S.A., Study investigation by methods of large parameter the systems of nonlinear difference-differential equations modeling predator-prey task, Doklady Akad. Nauk SSSR, 1982, vol. 266, pp. 792–795.
Grigorieva, E.V., Haken, H., and Kaschenko, S.A., Theory of quasiperiodicity in model of lasers with delayed optoelectronic feedback, Optics Commun., 1999, vol. 165, pp. 279–292.
Bestehorn, M., Grigorieva, E.V., Haken, H., and Kaschenko, S.A., Order parameters for class-B lasers with a long time delayed feedback, Physica D, 2000, vol. 145, pp. 111–129.
Kaschenko, S.A., Application of normalization method to study the dynamics of differential-difference equations with a small factor at derivative, Diff. Equat., 1989, vol. 25, pp. 1448–1451.
Kaschenko, S.A., On the quasi-normal forms for parabolic equations with small diffusion, Dokl. Akad. Nauk SSSR, 1988, vol. 299, pp. 1049–1053.
Kaschenko, S.A., On the short-wave bifurcations in systems with small diffusion, Dokl. Akad. Nauk SSSR, 1989, vol. 307, pp. 269–273.
Kaschenko, S.A., Ginzburg-Landau equation as the normal form for difference-differential equation of second order with a long delay, Zh. Vychisl. Matem. Matem. Fiz., 1998, vol. 38, pp. 457–465.
New in Synergetics: A Look into the Third Millennium, Makarov, I.M., Ed., Moscow: Nauka, 2002.
Kaschenko I.S. Local dynamics equations with a large delay, J. Compt. Mathem. Mathem. Phys., 2008, vol. 48, pp. 2141–2150.
Wolfrum, M. and Yanchuk, S., Eckhaus instability in systems with large delay, Phys. Rev. Lett., 2006, vol. 96, p. 220201.
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Grigorieva, E.V., Kashchenko, I.S. & Kashchenko, S.A. Multistability in a laser model with large delay. Aut. Control Comp. Sci. 48, 623–629 (2014). https://doi.org/10.3103/S0146411614070220
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DOI: https://doi.org/10.3103/S0146411614070220