Local dynamics of DDE with large delay in the vicinity of the self-similar cycle
Modelirovanie i analiz informacionnyh sistem, Tome 17 (2010) no. 3, pp. 38-47.

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We research the local dynamics of a complex differential equation with large delay in the vicinity of the self-similar cycle. The quasinormal forms method is used for a problem analysis.
Keywords: delay differential equation, periodic solution, normal form, small parameter.
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D. V. Glazkov; S. A. Kashchenko. Local dynamics of DDE with large delay in the vicinity of the self-similar cycle. Modelirovanie i analiz informacionnyh sistem, Tome 17 (2010) no. 3, pp. 38-47. http://geodesic.mathdoc.fr/item/MAIS_2010_17_3_a2/

[1] S. Schikora et al., “All-Optical Noninvasive Control of Unstable Steady States in a Semiconductor Laser”, Phys. Rev. Lett., 97 (2006), 213902, 4 pp. | DOI

[2] D. V. Glazkov, “Osobennosti dinamiki modeli Langa-Kobayashi v odnom kriticheskom sluchae”, Modelirovanie i analiz informatsionnykh sistem, 15:2 (2008), 36–45 | MR

[3] P. Hövel, E. Schöll, “Control of unstable steady states by time-delayed feedback methods”, Phys. Rev. E, 72 (2005), 046203, 7 pp. | DOI

[4] S. Yanchuk et al., “Control of unstable steady states by long delay feedback”, Phys. Rev. E, 74 (2006), 026201, 7 pp. | DOI | MR

[5] S. A. Kaschenko, “Bifurkatsii tsikla v singulyarno vozmuschennykh nelineinykh avtonomnykh sistemakh”, Izvestiya RAEN. Seriya MMMIU, 2:4 (1998), 5–53

[6] G. H. M. Van Tartwijk, D. Lenstra, “Nonlocal potential for class-B lasers with external optical feedback”, Phys. Rev. A, 50:4 (1994), 2837–2840

[7] C. Masoller, “Noise-Induced Resonance in Delayed Feedback Systems”, Phys. Rev. Lett., 88:3 (2002), 034102, 4 pp. | DOI

[8] D. V. Glazkov, “Normalizatsiya odnogo uravneniya zapazdyvaniem i bifurkatsiya, privodyaschaya k tsiklu asimptoticheski bolshogo perioda”, Modelirovanie i analiz informatsionnykh sistem, 14:2 (2007), 47–52 | MR