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Volumn 4, Issue 3, 2005, Pages 607-648

Geometric singular perturbation analysis of the Yamada model

Author keywords

Blow up method; Homoclinic orbits; Laser dynamics; Slow fast dynamics

Indexed keywords

BIFURCATION (MATHEMATICS); GEOMETRY; LASERS; PERTURBATION TECHNIQUES;

EID: 33644911236     PISSN: 15360040     EISSN: 15360040     Source Type: Journal    
DOI: 10.1137/040604820     Document Type: Article
Times cited : (20)

References (29)
  • 2
    • 0035446159 scopus 로고    scopus 로고
    • Dimensionless rate equations and simple conditions for self-pulsing in laser diodes
    • T. CARR AND T. ERNEUX, Dimensionless rate equations and simple conditions for self-pulsing in laser diodes, IEEE J. Quant. Electr., 37 (2001), pp. 1171-1177.
    • (2001) IEEE J. Quant. Electr. , vol.37 , pp. 1171-1177
    • Carr, T.1    Erneux, T.2
  • 4
    • 0002336002 scopus 로고
    • Techniques in the theory of local bifurcations: Blow up, normal forms, nilpotent bifurcations, singular perturbations
    • Kluwer, Dordrecht
    • F. DUMORTIER, Techniques in the theory of local bifurcations: Blow up, normal forms, nilpotent bifurcations, singular perturbations, in Bifurcations and Periodic Orbits of Vector Fields, Kluwer, Dordrecht, 1993, pp. 19-73.
    • (1993) Bifurcations and Periodic Orbits of Vector Fields , pp. 19-73
    • Dumortier, F.1
  • 6
    • 0035920091 scopus 로고    scopus 로고
    • Multiple canard cycles in generalized Lienard equations
    • F. DUMORTIER AND R. ROUSSARIE, Multiple canard cycles in generalized Lienard equations, J. Differential Equations, 174 (2001), pp. 1-29.
    • (2001) J. Differential Equations , vol.174 , pp. 1-29
    • Dumortier, F.1    Roussarie, R.2
  • 7
    • 84975583241 scopus 로고
    • Q-switching bifurcation in a laser with a saturable absorber
    • T. ERNEUX, Q-switching bifurcation in a laser with a saturable absorber, J. Opt. Soc. Amer. B Opt. Phys., 5 (1988), pp. 1063-1069.
    • (1988) J. Opt. Soc. Amer. B Opt. Phys. , vol.5 , pp. 1063-1069
    • Erneux, T.1
  • 8
    • 0000874353 scopus 로고    scopus 로고
    • Multiple time scale analysis of lasers
    • Fundamental Issues of Nonlinear Laser Dynamics, Amer. Inst. Phys., New York
    • T. ERNEUX, Multiple time scale analysis of lasers, in Fundamental Issues of Nonlinear Laser Dynamics, AIP Conf. Proc. 548, Amer. Inst. Phys., New York, 2000, pp. 54-65.
    • (2000) AIP Conf. Proc. , vol.548 , pp. 54-65
    • Erneux, T.1
  • 13
    • 0041975809 scopus 로고    scopus 로고
    • Singular Hopf bifurcation to strongly pulsating oscillations in lasers containing a saturable absorber
    • G. KOZYREFF AND T. ERNEUX, Singular Hopf bifurcation to strongly pulsating oscillations in lasers containing a saturable absorber, European J. Appl. Math., 14 (2003), pp. 407-420.
    • (2003) European J. Appl. Math. , vol.14 , pp. 407-420
    • Kozyreff, G.1    Erneux, T.2
  • 14
    • 0032751970 scopus 로고    scopus 로고
    • Self-pulsation of lasers with saturable absorber: Dynamics and bifurcations
    • J. DUBBELDAM AND B. KRAUSKOPF, Self-pulsation of lasers with saturable absorber: Dynamics and bifurcations. Opt. Commun., 159 (1999), pp. 325-338.
    • (1999) Opt. Commun. , vol.159 , pp. 325-338
    • Dubbeldam, J.1    Krauskopf, B.2
  • 15
    • 0001243959 scopus 로고    scopus 로고
    • Excitability and coherence resonance in lasers with saturable absorber
    • J. DUBBELDAM, B. KRAUSKOPF, AND D. LENSTRA, Excitability and coherence resonance in lasers with saturable absorber, Phys. Rev. E (3), 60 (1999), pp. 6580-6588.
    • (1999) Phys. Rev. E (3) , vol.60 , pp. 6580-6588
    • Dubbeldam, J.1    Krauskopf, B.2    Lenstra, D.3
  • 16
    • 34250627892 scopus 로고
    • Geometric singular perturbation theory
    • N. FENICHEL, Geometric singular perturbation theory, J. Differential Equations, 31 (1979), pp. 53-98.
    • (1979) J. Differential Equations , vol.31 , pp. 53-98
    • Fenichel, N.1
  • 18
    • 0002316532 scopus 로고
    • Geometric singular perturbation theory
    • Dynamical Systems, Springer-Verlag, New York
    • C. K. R. T. JONES, Geometric singular perturbation theory, in Dynamical Systems, Lecture Notes Math. 1609, Springer-Verlag, New York, 1995, pp. 44-120.
    • (1995) Lecture Notes Math. , vol.1609 , pp. 44-120
    • Jones, C.K.R.T.1
  • 19
    • 33749317702 scopus 로고    scopus 로고
    • A primer on the exchange lemma for fast-slow systems
    • Multiple-Time-Scale Dynamical Systems, Springer-Verlag, New York
    • C. JONES AND T. KAPER, A primer on the exchange lemma for fast-slow systems, in Multiple-Time-Scale Dynamical Systems, IMA Vol. Math. Appl. 122, Springer-Verlag, New York, 2001, pp. 65-87.
    • (2001) IMA Vol. Math. Appl. , vol.122 , pp. 65-87
    • Jones, C.1    Kaper, T.2
  • 20
    • 0000874351 scopus 로고    scopus 로고
    • Fundamental issues of nonlinear laser dynamics
    • Amer. Inst. Phys., New York
    • B. KRAUSKOPF AND D. LENSTRA, Fundamental Issues of Nonlinear Laser Dynamics, AIP Conf. Proc. 548, Amer. Inst. Phys., New York, 2000.
    • (2000) AIP Conf. Proc. , vol.548
    • Krauskopf, B.1    Lenstra, D.2
  • 21
    • 0033243360 scopus 로고    scopus 로고
    • Experimentally confirmed design guidelines for passively Q-switched microchip lasers using semiconductor saturable absorbers
    • G. J. SPÜHLER, R. PASCHOTTA, R. FLUCK, B. BRAUN, M. MOSER, G. ZHANG, E. GINI, AND U. KELLER, Experimentally confirmed design guidelines for passively Q-switched microchip lasers using semiconductor saturable absorbers, J. Opt. Soc. Amer. B Opt. Phys., 16 (1999), pp. 376-388.
    • (1999) J. Opt. Soc. Amer. B Opt. Phys. , vol.16 , pp. 376-388
    • Spühler, G.J.1    Paschotta, R.2    Fluck, R.3    Braun, B.4    Moser, M.5    Zhang, G.6    Gini, E.7    Keller, U.8
  • 22
    • 0036052772 scopus 로고    scopus 로고
    • Extending geometric singular perturbation theory to nonhyperbolic pointsfold and canard points in two dimensions
    • M. KRUPA AND P. SZMOLYAN, Extending geometric singular perturbation theory to nonhyperbolic pointsfold and canard points in two dimensions, SIAM J. Math. Anal., 33 (2001), pp. 286-314.
    • (2001) SIAM J. Math. Anal. , vol.33 , pp. 286-314
    • Krupa, M.1    Szmolyan, P.2
  • 23
    • 0035511458 scopus 로고    scopus 로고
    • Extending slow manifolds near transcritical and pitchfork singularities
    • M. KRUPA AND P. SZMOLYAN, Extending slow manifolds near transcritical and pitchfork singularities, Nonlinearity, 14 (2001), pp. 1473-1491.
    • (2001) Nonlinearity , vol.14 , pp. 1473-1491
    • Krupa, M.1    Szmolyan, P.2
  • 25
    • 0000152319 scopus 로고
    • Partially hyperbolic fixed points
    • F. TAKENS, Partially hyperbolic fixed points, Topology, 10 (1971), pp. 133-147.
    • (1971) Topology , vol.10 , pp. 133-147
    • Takens, F.1
  • 28
    • 0027593434 scopus 로고
    • A theoretical analysis of self-sustained pulsation phenomena in narrow-stripe semiconductor lasers
    • M. YAMADA, A theoretical analysis of self-sustained pulsation phenomena in narrow-stripe semiconductor lasers, IEEE J. Quant. Electr., 29 (1993), pp. 1330-1336.
    • (1993) IEEE J. Quant. Electr. , vol.29 , pp. 1330-1336
    • Yamada, M.1
  • 29
    • 0001245760 scopus 로고    scopus 로고
    • Ultraviolet generation with passively Q-switched microchip lasers
    • J. J. ZAYHOWSKI, Ultraviolet generation with passively Q-switched microchip lasers, Opt. Lett., 21 (1996), pp. 588-590.
    • (1996) Opt. Lett. , vol.21 , pp. 588-590
    • Zayhowski, J.J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.