메뉴 건너뛰기




Volumn 35, Issue 3, 2015, Pages 762-834

A proof of the Kuramoto conjecture for a bifurcation structure of the infinite-dimensional Kuramoto model

Author keywords

[No Author keywords available]

Indexed keywords


EID: 84928104636     PISSN: 01433857     EISSN: 14694417     Source Type: Journal    
DOI: 10.1017/etds.2013.68     Document Type: Review
Times cited : (97)

References (45)
  • 2
    • 0032046326 scopus 로고    scopus 로고
    • Asymptotic description of transients and synchronized states of globally coupled oscillators
    • J. A. Acebrón and L. L. Bonilla. Asymptotic description of transients and synchronized states of globally coupled oscillators. Phys. D 114(3-4) (1998), 296-314.
    • (1998) Phys. D , vol.114 , Issue.3-4 , pp. 296-314
    • Acebrón, J.A.1    Bonilla, L.L.2
  • 4
    • 0040183943 scopus 로고    scopus 로고
    • A shocking display of synchrony
    • N. J. Balmforth and R. Sassi. A shocking display of synchrony. Phys. D 143(1-4) (2000), 21-55.
    • (2000) Phys. D , vol.143 , Issue.1-4 , pp. 21-55
    • Balmforth, N.J.1    Sassi, R.2
  • 5
    • 0002538743 scopus 로고
    • Invariant manifolds for semilinear partial differential equations
    • John Wiley, Chichester
    • P. W. Bates and C. K. R. T. Jones. Invariant manifolds for semilinear partial differential equations. Dynamics Reported. Vol. 2. John Wiley, Chichester, 1989, pp. 1-38.
    • (1989) Dynamics Reported , vol.2 , pp. 1-38
    • Bates, P.W.1    Jones, C.K.R.T.2
  • 6
    • 0001063041 scopus 로고
    • Nonlinear stability of incoherence and collective synchronization in a population of coupled oscillators
    • L. L. Bonilla, J. C. Neu and R. Spigler. Nonlinear stability of incoherence and collective synchronization in a population of coupled oscillators. J. Stat. Phys. 67(1-2) (1992), 313-330.
    • (1992) J. Stat. Phys. , vol.67 , Issue.1-2 , pp. 313-330
    • Bonilla, L.L.1    Neu, J.C.2    Spigler, R.3
  • 7
    • 22244479715 scopus 로고    scopus 로고
    • Time-periodic phases in populations of nonlinearly coupled oscillators with bimodal frequency distributions
    • L. L. Bonilla, C. J. Pérez Vicente and R. Spigler. Time-periodic phases in populations of nonlinearly coupled oscillators with bimodal frequency distributions. Phys. D 113(1) (1998), 79-97.
    • (1998) Phys. D , vol.113 , Issue.1 , pp. 79-97
    • Bonilla, L.L.1    Pérez Vicente, C.J.2    Spigler, R.3
  • 8
    • 0040652275 scopus 로고    scopus 로고
    • Invariant foliations for C 1 semigroups in Banach spaces
    • X.-Y. Chen, J. K. Hale and T. Bin. Invariant foliations for C 1 semigroups in Banach spaces. J. Differential Equations 139(2) (1997), 283-318.
    • (1997) J. Differential Equations , vol.139 , Issue.2 , pp. 283-318
    • Chen, X.-Y.1    Hale, J.K.2    Bin, T.3
  • 9
    • 84855292010 scopus 로고    scopus 로고
    • Center manifold reduction for a large population of globally coupled phase oscillators
    • H. Chiba and I. Nishikawa. Center manifold reduction for a large population of globally coupled phase oscillators. Chaos 21 (2011).
    • (2011) Chaos , vol.21
    • Chiba, H.1    Nishikawa, I.2
  • 10
    • 84872138052 scopus 로고    scopus 로고
    • Continuous limit and the moments system for the globally coupled phase oscillators
    • H. Chiba. Continuous limit and the moments system for the globally coupled phase oscillators. Discrete. Contin. Dyn. Syst. 33 (2013), 1891-1903.
    • (2013) Discrete. Contin. Dyn. Syst. , vol.33 , pp. 1891-1903
    • Chiba, H.1
  • 11
    • 67349214431 scopus 로고    scopus 로고
    • Stability of an [N/2]-dimensional invariant torus in the Kuramoto model at small coupling
    • H. Chiba and D. Pazó. Stability of an [N/2]-dimensional invariant torus in the Kuramoto model at small coupling. Phys. D 238 (2009), 1068-1081.
    • (2009) Phys. D , vol.238 , pp. 1068-1081
    • Chiba, H.1    Pazó, D.2
  • 12
    • 21344481602 scopus 로고
    • Amplitude expansions for instabilities in populations of globally-coupled oscillators
    • J. D. Crawford. Amplitude expansions for instabilities in populations of globally-coupled oscillators. J. Stat. Phys. 74(5-6) (1994), 1047-1084.
    • (1994) J. Stat. Phys. , vol.74 , Issue.5-6 , pp. 1047-1084
    • Crawford, J.D.1
  • 13
    • 0012588411 scopus 로고
    • Scaling and singularities in the entrainment of globally coupled oscillators
    • J. D. Crawford. Scaling and singularities in the entrainment of globally coupled oscillators. Phys. Rev. Lett. 74 (1995), 4341-4344.
    • (1995) Phys. Rev. Lett. , vol.74 , pp. 4341-4344
    • Crawford, J.D.1
  • 14
    • 0032633546 scopus 로고    scopus 로고
    • Synchronization of globally coupled phase oscillators: Singularities and scaling for general couplings
    • J. D. Crawford and K. T. R. Davies. Synchronization of globally coupled phase oscillators: singularities and scaling for general couplings. Phys. D 125(1-2) (1999), 1-46.
    • (1999) Phys. D , vol.125 , Issue.1-2 , pp. 1-46
    • Crawford, J.D.1    Davies, K.T.R.2
  • 17
    • 0003888215 scopus 로고
    • Gordon and Breach Science Publishers, New York-London-Paris
    • A. Grothendieck. Topological Vector Spaces. Gordon and Breach Science Publishers, New York-London-Paris, 1973.
    • (1973) Topological Vector Spaces
    • Grothendieck, A.1
  • 20
    • 84972496069 scopus 로고
    • Projective and injective limits of weakly compact sequences of locally convex spaces
    • H. Komatsu. Projective and injective limits of weakly compact sequences of locally convex spaces. J. Math. Soc. Japan 19 (1967), 366-383.
    • (1967) J. Math. Soc. Japan , vol.19 , pp. 366-383
    • Komatsu, H.1
  • 21
    • 18744410379 scopus 로고    scopus 로고
    • Invariance and noninvariance of center manifolds of time-t maps with respect to the semiflow
    • T. Krisztin. Invariance and noninvariance of center manifolds of time-t maps with respect to the semiflow. SIAM J. Math. Anal. 36(3) (2004/05), 717-739.
    • (2004) SIAM J. Math. Anal. , vol.36 , Issue.3 , pp. 717-739
    • Krisztin, T.1
  • 24
    • 19544377328 scopus 로고    scopus 로고
    • Mechanism of desynchronization in the finite-dimensional Kuramoto model
    • Y. Maistrenko, O. Popovych, O. Burylko and P. A. Tass. Mechanism of desynchronization in the finite-dimensional Kuramoto model. Phys. Rev. Lett. 93 (2004).
    • (2004) Phys. Rev. Lett. , vol.93
    • Maistrenko, Y.1    Popovych, O.2    Burylko, O.3    Tass, P.A.4
  • 28
    • 74349098541 scopus 로고    scopus 로고
    • Identical phase oscillators with global sinusoidal coupling evolve by Mobius group action
    • S. A. Marvel, R. E. Mirollo and S. H. Strogatz. Identical phase oscillators with global sinusoidal coupling evolve by Mobius group action. Chaos 19 (2009).
    • (2009) Chaos , vol.19
    • Marvel, S.A.1    Mirollo, R.E.2    Strogatz, S.H.3
  • 29
    • 34147192429 scopus 로고
    • Amplitude death in an array of limit-cycle oscillators
    • R. E. Mirollo and S. H. Strogatz. Amplitude death in an array of limit-cycle oscillators. J. Stat. Phys. 60(1-2) (1990), 245-262.
    • (1990) J. Stat. Phys. , vol.60 , Issue.1-2 , pp. 245-262
    • Mirollo, R.E.1    Strogatz, S.H.2
  • 30
    • 84867963225 scopus 로고    scopus 로고
    • The spectrum of the partially locked state for the Kuramoto model
    • R. Mirollo and S. H. Strogatz. The spectrum of the partially locked state for the Kuramoto model. J. Nonlinear Sci. 17(4) (2007), 309-347.
    • (2007) J. Nonlinear Sci. , vol.17 , Issue.4 , pp. 309-347
    • Mirollo, R.1    Strogatz, S.H.2
  • 31
    • 54749126999 scopus 로고    scopus 로고
    • Low dimensional behavior of large systems of globally coupled oscillators
    • E. Ott and T. M. Antonsen. Low dimensional behavior of large systems of globally coupled oscillators. Chaos 18(3) (2008).
    • (2008) Chaos , vol.18 , Issue.3
    • Ott, E.1    Antonsen, T.M.2
  • 32
    • 67651092270 scopus 로고    scopus 로고
    • Long time evolution of phase oscillator systems
    • E. Ott and T. M. Antonsen. Long time evolution of phase oscillator systems. Chaos 19(2) (2009).
    • (2009) Chaos , vol.19 , Issue.2
    • Ott, E.1    Antonsen, T.M.2
  • 38
    • 0039592729 scopus 로고    scopus 로고
    • From Kuramoto to Crawford: Exploring the onset of synchronization in populations of coupled oscillators
    • S. H. Strogatz. From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators. Phys. D 143(1-4) (2000), 1-20.
    • (2000) Phys. D , vol.143 , Issue.1-4 , pp. 1-20
    • Strogatz, S.H.1
  • 39
    • 1542499302 scopus 로고
    • Stability of incoherence in a population of coupled oscillators
    • S. H. Strogatz and R. E. Mirollo. Stability of incoherence in a population of coupled oscillators. J. Stat. Phys. 63(3-4) (1991), 613-635.
    • (1991) J. Stat. Phys. , vol.63 , Issue.3-4 , pp. 613-635
    • Strogatz, S.H.1    Mirollo, R.E.2
  • 40
    • 4243765520 scopus 로고
    • Coupled nonlinear oscillators below the synchronization threshold: Relaxation by generalized Landau damping
    • S. H. Strogatz, R. E. Mirollo and P. C. Matthews. Coupled nonlinear oscillators below the synchronization threshold: relaxation by generalized Landau damping. Phys. Rev. Lett. 68(18) (1992), 2730-2733.
    • (1992) Phys. Rev. Lett. , vol.68 , Issue.18 , pp. 2730-2733
    • Strogatz, S.H.1    Mirollo, R.E.2    Matthews, P.C.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.