Global bifurcations in a laser with injected signal: Beyond Adler's approximation
We discuss the dynamics in the laser with an injected signal from a perturbative point of view showing how different aspects of the dynamics get their definitive character at different orders in the perturbation scheme. At the lowest order Adler's equation [Proc. IRE 34, 351 (1946)] is recovere...
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American Institute of Physics Inc.
2001
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| LEADER | 05678caa a22006137a 4500 | ||
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| 024 | 7 | |2 scopus |a 2-s2.0-0035621095 | |
| 040 | |a Scopus |b spa |c AR-BaUEN |d AR-BaUEN | ||
| 100 | 1 | |a Zimmermann, M.G. | |
| 245 | 1 | 0 | |a Global bifurcations in a laser with injected signal: Beyond Adler's approximation |
| 260 | |b American Institute of Physics Inc. |c 2001 | ||
| 270 | 1 | 0 | |m Zimmermann, M.G.; Departamento de Física, Fac. Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina; email: zeta@df.uba.ar |
| 506 | |2 openaire |e Política editorial | ||
| 504 | |a Adler, R., (1946) Proc. IRE, 34, p. 351 | ||
| 504 | |a (1973) Proc. IEEE, 61, p. 1380 | ||
| 504 | |a Solari, H.G., Oppo, G.-L., (1994) Opt. Commun., 111, p. 173 | ||
| 504 | |a Jagher, P.C.D., Van Der Graaf, W.A., Lenstra, D., (1996) Quantum Semiclassic. Opt., 8, p. 805 | ||
| 504 | |a Krauskopf, B., Van Der Graaf, W.A., Lenstra, D., (1997) Quantum Semiclassic. Opt., 9, p. 797 | ||
| 504 | |a Zimmermann, M.G., Natiello, M.A., Solari, H.G., (1997) Physica D, 109, p. 293 | ||
| 504 | |a Mayol, C., Natiello, M.A., Zimmermann, M.G., Int. J. Bifur. Chaos, , in press | ||
| 504 | |a Tredicce, J.R., Arecchi, F.T., Lippi, G.-L., Puccioni, G.P., (1985) J. Opt. Soc. Am. B, 2, p. 173 | ||
| 504 | |a Kuznetsov, Y., Elements of applied bifurcation theory (1997) Applied Mathematical Sciences, 112. , Springer-Verlag, Berlin | ||
| 504 | |a Oppo, G.-L., Politi, A., Lippi, G.-L., Arecchi, F.T., (1986) Phys. Rev. A, 34, p. 4000 | ||
| 504 | |a Zeglache, H., Zehblè, V., (1992) Phys. Rev. A, 46, p. 6015 | ||
| 504 | |a Lugiato, L.A., Narducci, L.M., Bandy, D.K., Pennise, C.A., (1983) Opt. Commun., 46, p. 64 | ||
| 504 | |a Politi, A., Oppo, G., Badii, R., (1986) Phys. Rev. A, 33, p. 4055 | ||
| 504 | |a Braza, P.A., Erneux, T., (1989) Phys. Rev. A, 40, p. 2539 | ||
| 504 | |a Guckenheimer, J., Holmes, P.J., (1983) Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, , Springer-Verlag, New York | ||
| 504 | |a Wiggins, S., (1991) Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2. , Text in Applied Mathematics Springer-Verlag, Berlin | ||
| 504 | |a Sil'nikov, L.P., (1966) Sov. Math. Dokl., 7, p. 155 | ||
| 504 | |a Yeung, M.K.S., Strogatz, S., (1998) Phys. Rev. E, 58, p. 4421. , see erratum ibid. 61, 2154 (2000) | ||
| 504 | |a Solari, H.G., Natiello, M., Mindlin, B.G., (1996) Nonlinear Dynamics: A Two-Way Trip from Physics to Math, , Institute of Physics, Bristol | ||
| 504 | |a note; note; Oppo, G.-L., Politi, A., (1985) Z. Phys. B : Condens. Matter, 59, p. 111 | ||
| 504 | |a note; Doedel, E., Kernévez, J., (1986) AUTO: Software for Continuation Problems in Ordinary Differential Equations With Applications, , Tech. Rep., Applied Mathematics, California Institute of Technology | ||
| 504 | |a note; Deng, B., (1992) Trans. Am. Math. Soc., 331, p. 15 | ||
| 504 | |a note; Gaspard, P., Wang, X.-J., (1987) J. Stat. Phys., 48, p. 151 | ||
| 504 | |a Hirschberg, P., Laing, C., (1995) Physica D, 89, p. 1 | ||
| 504 | |a note; Wittenberg, R.W., Holmes, P., (1997) Physica D, 100, p. 1 | ||
| 520 | 3 | |a We discuss the dynamics in the laser with an injected signal from a perturbative point of view showing how different aspects of the dynamics get their definitive character at different orders in the perturbation scheme. At the lowest order Adler's equation [Proc. IRE 34, 351 (1946)] is recovered. More features emerge at first order including some bifurcations sets and the global reinjection conjectured in Physica D 109, 293 (1997). The type of codimension-2 bifurcations present can only be resolved at second order. We show that of the two averaging approximations proposed [Opt. Commun, 111, 173 (1994); Quantum Semiclassic. Opt. 9, 797 (1997); Quantum Semiclassic. Opt. 8, 805 (1996)] differing in the second order terms, only one is accurate to the order required, hence, solving the apparent contradiction among these results. We also show in numerical studies how a homoclinic orbit of the Sil'nikov type, bifurcates into a homoclinic tangency of a periodic orbit of vanishing amplitude. The local vector field at the transition point contains a Hopf-saddle-node singularity, which becomes degenerate and changes type. The overall global bifurcation is of codimension-3. The parameter governing this transition is 6, the cavity detuning (with respect to the atomic frequency) of the laser. © 2007 American Institute of Physics. |l eng | |
| 593 | |a Departamento de Física, Fac. Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina | ||
| 593 | |a Ctr. for Mathematical Sciences (LTH), Lund University, S-221 00 Lund, Sweden | ||
| 700 | 1 | |a Natiello, M.A. | |
| 700 | 1 | |a Solari, H.G. | |
| 773 | 0 | |d American Institute of Physics Inc., 2001 |g v. 11 |h pp. 500-513 |k n. 3 |p Chaos |x 10541500 |w (AR-BaUEN)CENRE-358 |t Chaos | |
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| 856 | 4 | 0 | |u https://hdl.handle.net/20.500.12110/paper_10541500_v11_n3_p500_Zimmermann |y Handle |
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