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Volumn 197, Issue 1, 2004, Pages 86-98

One-dimensional unstable eigenfunction and manifold computations in delay differential equations

Author keywords

Intermittent transition; Numerical tools for DDEs; PCF laser

Indexed keywords

CHAOS THEORY; DIFFERENTIAL EQUATIONS; SEMICONDUCTOR LASERS;

EID: 2942567779     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jcp.2003.11.018     Document Type: Article
Times cited : (16)

References (29)
  • 1
    • 0042590816 scopus 로고    scopus 로고
    • A report on the use of delay differential equations in numerical modelling in the biosciences
    • Technical Report 343, Department of Mathematics, University of Manchester, July
    • C.T.H. Baker, G.A. Bocharov, F.A. Rihan, A report on the use of delay differential equations in numerical modelling in the biosciences, Technical Report 343, Department of Mathematics, University of Manchester, July 1999.
    • (1999)
    • Baker, C.T.H.1    Bocharov, G.A.2    Rihan, F.A.3
  • 2
    • 2942586196 scopus 로고    scopus 로고
    • Chaos in periodically driven systems
    • B. Krauskopf, D. Lenstra (Eds.), AIP Conf. Proc
    • H.W. Broer, B. Krauskopf, Chaos in periodically driven systems, in: B. Krauskopf, D. Lenstra (Eds.), Fundamental Issues of Nonlinear Laser Dynamics, AIP Conf. Proc., vol. 548, 2000, pp. 31-53.
    • (2000) Fundamental Issues of Nonlinear Laser Dynamics , vol.548 , pp. 31-53
    • Broer, H.W.1    Krauskopf, B.2
  • 4
    • 0003636817 scopus 로고    scopus 로고
    • One-parameter Semigroups for Linear Evolution Equations
    • Springer, New York
    • K.J. Engel, R. Nagel, One-parameter Semigroups for Linear Evolution Equations, Graduate Texts in Mathematics, vol. 194, Springer, New York, 2000.
    • (2000) Graduate Texts in Mathematics , vol.194
    • Engel, K.J.1    Nagel, R.2
  • 5
    • 0035319009 scopus 로고    scopus 로고
    • Numerical bifurcation analysis of delay differential equations arising from physiological modeling
    • K. Engelborghs, V. Lemaire, J. Bélair, D. Roose, Numerical bifurcation analysis of delay differential equations arising from physiological modeling, J. Math. Biol. 42 (2001) 361-385.
    • (2001) J. Math. Biol. , vol.42 , pp. 361-385
    • Engelborghs, K.1    Lemaire, V.2    Bélair, J.3    Roose, D.4
  • 6
    • 0034770393 scopus 로고    scopus 로고
    • Collocation methods for the computation of periodic solutions of delay differential equations
    • K. Engelborghs, T. Luzyanina, K. in't Hout, D. Roose, Collocation methods for the computation of periodic solutions of delay differential equations, SIAM J. Sci. Comput. 22 (2000) 1593-1609.
    • (2000) SIAM J. Sci. Comput. , vol.22 , pp. 1593-1609
    • Engelborghs, K.1    Luzyanina, T.2    in't Hout, K.3    Roose, D.4
  • 7
    • 0004033107 scopus 로고    scopus 로고
    • DDE-BIFTOOL v2.00: A Matlab package for bifurcation analysis of delay differential equations
    • Technical Report TW-330, Department of Computer Science, K.U. Leuven, Belgium, Available from:
    • K. Engelborghs, T. Luzyanina, G. Samaey, DDE-BIFTOOL v2.00: a Matlab package for bifurcation analysis of delay differential equations, Technical Report TW-330, Department of Computer Science, K.U. Leuven, Belgium, 2000. Available from: .
    • (2000)
    • Engelborghs, K.1    Luzyanina, T.2    Samaey, G.3
  • 9
    • 84975568518 scopus 로고
    • Mode locking in semiconductor lasers by phase-conjugate optical feedback
    • G.R. Gray, D.H. DeTienne, G.P. Agrawal, Mode locking in semiconductor lasers by phase-conjugate optical feedback, Opt. Lett. 20 (1995) 1295- 1297.
    • (1995) Opt. Lett. , vol.20 , pp. 1295-1297
    • Gray, G.R.1    DeTienne, D.H.2    Agrawal, G.P.3
  • 10
    • 0028387753 scopus 로고
    • Chaotic dynamics of semiconductor lasers with phase-conjugate feedback
    • G.R. Gray, D. Huang, G.P. Agrawal, Chaotic dynamics of semiconductor lasers with phase-conjugate feedback, Phys. Rev. A 49 (1994) 2096-2105.
    • (1994) Phys. Rev. A , vol.49 , pp. 2096-2105
    • Gray, G.R.1    Huang, D.2    Agrawal, G.P.3
  • 11
    • 24544478068 scopus 로고
    • Critical exponents for crisis-induced intermittency
    • C. Grebogi, E. Ott, F. Romeiras, J.A. Yorke, Critical exponents for crisis-induced intermittency, Phys. Rev. A 36 (1987) 5365-5380.
    • (1987) Phys. Rev. A , vol.36 , pp. 5365-5380
    • Grebogi, C.1    Ott, E.2    Romeiras, F.3    Yorke, J.A.4
  • 12
    • 2942587999 scopus 로고    scopus 로고
    • Software for computing unstable manifolds of delay differential equations
    • Technical Report TW-377, Department of Computer Science, K.U. Leuven, Belgium
    • K. Green, B. Krauskopf, D. Roose, Software for computing unstable manifolds of delay differential equations, Technical Report TW-377, Department of Computer Science, K.U. Leuven, Belgium, 2003.
    • (2003)
    • Green, K.1    Krauskopf, B.2    Roose, D.3
  • 13
    • 0242593138 scopus 로고    scopus 로고
    • Bifurcation analysis of frequency locking in a semiconductor laser with phase-conjugate feedback
    • K. Green, B. Krauskopf, Bifurcation analysis of frequency locking in a semiconductor laser with phase-conjugate feedback, Int. J. Bifurc. Chaos 13 (9) (2003) 2589-2601.
    • (2003) Int. J. Bifurc. Chaos , vol.13 , Issue.9 , pp. 2589-2601
    • Green, K.1    Krauskopf, B.2
  • 14
    • 37649030953 scopus 로고    scopus 로고
    • Global bifurcations and bistability at the locking boundaries of a semiconductor laser with phase-conjugate feedback
    • (016220)
    • K. Green, B. Krauskopf, Global bifurcations and bistability at the locking boundaries of a semiconductor laser with phase-conjugate feedback, Phys. Rev. E 66 (016220) (2002).
    • (2002) Phys. Rev. E , vol.66
    • Green, K.1    Krauskopf, B.2
  • 15
    • 0036888252 scopus 로고    scopus 로고
    • Bistability and torus break-up in a semiconductor laser with phase-conjugate feedback
    • K. Green, B. Krauskopf, K. Engelborghs, Bistability and torus break-up in a semiconductor laser with phase-conjugate feedback, Physica D 173 (2002) 114-129.
    • (2002) Physica D , vol.173 , pp. 114-129
    • Green, K.1    Krauskopf, B.2    Engelborghs, K.3
  • 16
    • 0347461231 scopus 로고    scopus 로고
    • A two-parameter study of the locking region of a semiconductor laser subject to phase-conjugate feedback
    • K. Green, B. Krauskopf, G. Samaey, A two-parameter study of the locking region of a semiconductor laser subject to phase-conjugate feedback, SIAM J. Appl. Dynamical Systems 2 (2) (2003) 254-276.
    • (2003) SIAM J. Appl. Dynamical Systems , vol.2 , Issue.2 , pp. 254-276
    • Green, K.1    Krauskopf, B.2    Samaey, G.3
  • 17
    • 41349099787 scopus 로고    scopus 로고
    • Stability and rupture of bifurcation bridges in semiconductor lasers subject to optical feedback
    • (046216)
    • B. Haegeman, K. Engelborghs, D. Roose, D. Pieroux, T. Erneux, Stability and rupture of bifurcation bridges in semiconductor lasers subject to optical feedback, Phys. Rev. E 66 (046216) (2002).
    • (2002) Phys. Rev. E , vol.66
    • Haegeman, B.1    Engelborghs, K.2    Roose, D.3    Pieroux, D.4    Erneux, T.5
  • 19
    • 0000725132 scopus 로고    scopus 로고
    • Semiconductor laser with phase-conjugate feedback: Dynamics and bifurcations
    • B. Krauskopf, G.R. Gray, D. Lenstra, Semiconductor laser with phase-conjugate feedback: dynamics and bifurcations, Phys. Rev. E 58 (1998) 7190-7196.
    • (1998) Phys. Rev. E , vol.58 , pp. 7190-7196
    • Krauskopf, B.1    Gray, G.R.2    Lenstra, D.3
  • 20
    • 0037456930 scopus 로고    scopus 로고
    • Computing unstable manifolds of periodic orbits in delay differential equations
    • B. Krauskopf, K. Green, Computing unstable manifolds of periodic orbits in delay differential equations, J. Comput. Phys. 186 (2003) 230-249.
    • (2003) J. Comput. Phys. , vol.186 , pp. 230-249
    • Krauskopf, B.1    Green, K.2
  • 22
    • 0000010680 scopus 로고    scopus 로고
    • Growing 1D and quasi 2D unstable manifolds of maps
    • B. Krauskopf, H.M. Osinga, Growing 1D and quasi 2D unstable manifolds of maps, J. Comput. Phys. 146 (1998) 404-419.
    • (1998) J. Comput. Phys. , vol.146 , pp. 404-419
    • Krauskopf, B.1    Osinga, H.M.2
  • 23
    • 0032016858 scopus 로고    scopus 로고
    • Globalizing two-dimensional unstable manifolds of maps
    • B. Krauskopf, H.M. Osinga, Globalizing two-dimensional unstable manifolds of maps, Int. J. Bifurc. Chaos 8 (1998) 483-503.
    • (1998) Int. J. Bifurc. Chaos , vol.8 , pp. 483-503
    • Krauskopf, B.1    Osinga, H.M.2
  • 24
    • 0036999840 scopus 로고    scopus 로고
    • Computing Floquet multipliers for functional differential equations
    • T. Luzyanina, K. Engelborghs, Computing Floquet multipliers for functional differential equations, Int. J. Bifurc. Chaos 12 (12) (2002) 2977-2989.
    • (2002) Int. J. Bifurc. Chaos , vol.12 , Issue.12 , pp. 2977-2989
    • Luzyanina, T.1    Engelborghs, K.2
  • 25
    • 45949127771 scopus 로고
    • Different ways to turbulence in dissipative dynamical systems
    • P. Manneville, Y. Pomeau, Different ways to turbulence in dissipative dynamical systems, Physica D 1 (2) (1980) 219-226.
    • (1980) Physica D , vol.1 , Issue.2 , pp. 219-226
    • Manneville, P.1    Pomeau, Y.2
  • 26
    • 0003475470 scopus 로고
    • Mathematical Biology
    • Springer, Berlin
    • J.D. Murray, Mathematical Biology, in: Biomathematics Texts, vol. 19, Springer, Berlin, 1980.
    • (1980) Biomathematics Texts , vol.19
    • Murray, J.D.1
  • 27
    • 0036541778 scopus 로고    scopus 로고
    • Bifurcation bridges between external-cavity modes lead to polarization self-modulation in vertical-cavity surface-emitting lasers
    • (041801(R))
    • M. Sciamanna, T. Erneux, F. Rogister, O. Deparis, P. Megret, M. Blondel, Bifurcation bridges between external-cavity modes lead to polarization self-modulation in vertical-cavity surface-emitting lasers, Phys. Rev. A 65 (041801(R)) (2002).
    • (2002) Phys. Rev. A , vol.65
    • Sciamanna, M.1    Erneux, T.2    Rogister, F.3    Deparis, O.4    Megret, P.5    Blondel, M.6
  • 29
    • 0002132449 scopus 로고    scopus 로고
    • The mathematics of delay equations with an application to the Lang-Kobayashi equations
    • B. Krauskopf, D. Lenstra (Eds.), AIP Conf. Proc
    • S.M. Verduyn Lunel, B. Krauskopf, The mathematics of delay equations with an application to the Lang-Kobayashi equations, in: B. Krauskopf, D. Lenstra (Eds.), Fundamental Issues of Nonlinear Laser Dynamics, AIP Conf. Proc., vol. 548, 2000, pp. 66-86.
    • (2000) Fundamental Issues of Nonlinear Laser Dynamics , vol.548 , pp. 66-86
    • Verduyn Lunel, S.M.1    Krauskopf, B.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.