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Stabilization of optically coupled lasers with periodic pumping

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Nonlinear Oscillations

We study a periodically forced system modeling the synchronization of two optically coupled lasers pumped by an alternating current. A necessary and sufficient condition for the existence of a periodic solution is given, as well as a sufficient condition for its uniqueness and asymptotic stability.

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References

  1. R. Roy and K. S. Thornburg, Jr., “Experimental synchronization of chaotic lasers,” Phys. Rev. Lett., 72, Issue 13, 2009–2012 (1994).

    Article  Google Scholar 

  2. V.V. Likhanskii and A. P. Napartovich, “Radiation emitted by optically coupled lasers,” Sov. Phys. Usp., 33, No. 3, 228–252 (1990).

    Article  Google Scholar 

  3. V.V. Likhanskii, A. P. Napartovich, and A. G. Sukharev, “Phase locking of optically coupled lasers with periodic pumping,” Kvant. Elektron., 22, No. 1, 47–48 (1995).

    Google Scholar 

  4. D. M. Lila and A. A. Martynyuk, “On stability of some solutions for equations of locked lasing of optically coupled lasers with periodic pumping,” Nonlin. Oscillations, 12, No. 4, 464–473 (2009).

    Article  MathSciNet  Google Scholar 

  5. A. A. Martynyuk, Stability of Motion. The Role of Multicomponent Liapunov Functions, Cambridge Sci. Publ., Cambridge (2007).

    Google Scholar 

  6. L. H. Erbe, “Stability results for periodic second order linear differential equations,” Proc. Am. Math. Soc., 93, No. 2, 272–276 (1985).

    Article  MathSciNet  MATH  Google Scholar 

  7. J. Mawhin and J. R. Ward, Jr., “Periodic solutions of some forced Liénard differential equations at resonance,” Arch. Math., 41, No. 4, 337–351 (1983).

    Article  MathSciNet  MATH  Google Scholar 

  8. A. Capietto, J. Mawhin, and F. Zanolin, “Continuation theorems for periodic perturbations of autonomous systems,” Trans. Am. Math. Soc., 329, 41–72 (1992).

    Article  MathSciNet  MATH  Google Scholar 

  9. L. Cesari, Asymptotic Behavior and Stability Problems in Ordinary Differential Equations, Springer, Berlin (1971).

    MATH  Google Scholar 

  10. M. Grau and D. Peralta-Salas, “A note on linear differential equations with periodic coefficients,” Nonlin. Anal., 71, 3197–3202 (2009).

    Article  MathSciNet  MATH  Google Scholar 

  11. A. Zitan and R. Ortega, “Existence of asymptotically stable periodic solutions of a forced equation of Liénard type,” Nonlin. Anal., 22, No. 8, 993–1003 (1994).

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Departamento de Matemática Aplicada, Universidad de Granada, Facultad de Ciencias, Granada, Spain

    P. J. Torres

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  1. P. J. Torres
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Correspondence to P. J. Torres.

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Published in Neliniini Kolyvannya, Vol. 14, No. 3, pp. 392–399, July–September, 2011.

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Torres, P.J. Stabilization of optically coupled lasers with periodic pumping. Nonlinear Oscill 14, 414–422 (2012). https://doi.org/10.1007/s11072-012-0166-4

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  • DOI: https://doi.org/10.1007/s11072-012-0166-4

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