메뉴 건너뛰기




Volumn 125, Issue 1-2, 1999, Pages 1-46

Synchronization of globally coupled phase oscillators: Singularities and scaling for general couplings

Author keywords

Bifurcation, Symmetry; Oscillators

Indexed keywords

BIFURCATION (MATHEMATICS); DYNAMICS; MATHEMATICAL MODELS; PROBLEM SOLVING; STABILITY; SYNCHRONIZATION;

EID: 0032633546     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(98)00235-8     Document Type: Article
Times cited : (91)

References (44)
  • 1
    • 0000747853 scopus 로고
    • Frequency plateaus in a chain of weakly coupled oscillators. I
    • G.B Ermentrout, N Kopell, Frequency plateaus in a chain of weakly coupled oscillators. I, SIAM J. Math Anal. 15 (1984) 215
    • (1984) SIAM J. Math Anal. , vol.15 , pp. 215
    • Ermentrout, G.B.1    Kopell, N.2
  • 3
    • 34249831818 scopus 로고    scopus 로고
    • The dynamics of n weakly coupled identical oscillators
    • R Ashwin, J W. Swift, The dynamics of n weakly coupled identical oscillators, J. Nonlinear Sci. 2 69
    • J. Nonlinear Sci. , pp. 269
    • Ashwin, R.1    Swift, J.W.2
  • 4
    • 0014108715 scopus 로고
    • Biological rhythms and the behavior of populations of coupled oscillators
    • A T. Winfree, Biological rhythms and the behavior of populations of coupled oscillators, J. Theoret. Biol. 16 (1967) 15-42.
    • (1967) J. Theoret. Biol. , vol.16 , pp. 15-42
    • Winfree, A.T.1
  • 6
    • 0001315407 scopus 로고
    • Norbert Wiener's Brain Waves
    • S. Levin (Ed), Springer, New York
    • S.H. Strogatz, Norbert Wiener's Brain Waves, in. S. Levin (Ed), Lecture Notes in Biomathematics, vol 100, Springer, New York, 1994.
    • (1994) Lecture Notes in Biomathematics , vol.100
    • Strogatz, S.H.1
  • 7
    • 0024514737 scopus 로고
    • Oscillatory responses in cat visual cortex exhibit inter-columnar synchronization which reflects global stimulus properties
    • C M. Gray, P Konig, A K. Engel, W Singer, Oscillatory responses in cat visual cortex exhibit inter-columnar synchronization which reflects global stimulus properties, Nature 338 (1989) 334-337
    • (1989) Nature , vol.338 , pp. 334-337
    • Gray, C.M.1    Konig, P.2    Engel, A.K.3    Singer, W.4
  • 8
    • 0001006240 scopus 로고    scopus 로고
    • Synchronization transitions in a disordered Josephson series array
    • K Wiesenfeld, P. Colet, S H Strogatz, Synchronization transitions in a disordered Josephson series array, Phys. Rev Lett 76 (1996) 404.
    • (1996) Phys. Rev Lett , vol.76 , pp. 404
    • Wiesenfeld, K.1    Colet, P.2    Strogatz, S.H.3
  • 10
    • 8744301263 scopus 로고
    • Averaged equations for Josephson junction series arrays
    • K. Wiesenfeld, J.W Swift, Averaged equations for Josephson junction series arrays, Physica D 55 (1992) 239.
    • (1992) Physica D , vol.55 , pp. 239
    • Wiesenfeld, K.1    Swift, J.W.2
  • 11
    • 0001551665 scopus 로고
    • Statistical macrodynamics of large dynamical systems Case of a phase transition in oscillator communities
    • Y Kuramoto, I Nishikawa, Statistical macrodynamics of large dynamical systems Case of a phase transition in oscillator communities, J Stat Phys. 49 (1987) 569-605
    • (1987) J Stat Phys. , vol.49 , pp. 569-605
    • Kuramoto, Y.1    Nishikawa, I.2
  • 12
    • 21144480274 scopus 로고
    • Phase dynamics for weakly coupled Hodgkin-Huxley neurons
    • D. Hansel, G. Mato, C Meunier, Phase dynamics for weakly coupled Hodgkin-Huxley neurons, Europhys Lett. 23 (1993) 367-372
    • (1993) Europhys Lett. , vol.23 , pp. 367-372
    • Hansel, D.1    Mato, G.2    Meunier, C.3
  • 13
    • 6044220638 scopus 로고
    • Generic scaling at the onset of macroscopic mutual entrainment in limit-cycle oscillators with uniform all-to-all coupling
    • H Daido, Generic scaling at the onset of macroscopic mutual entrainment in limit-cycle oscillators with uniform all-to-all coupling, Phys. Rev Lett 73 (1994) 760-763
    • (1994) Phys. Rev Lett , vol.73 , pp. 760-763
    • Daido, H.1
  • 14
    • 0012588411 scopus 로고
    • Scaling and singularities in the entranment of globally coupled oscillators
    • J.D Crawford, Scaling and singularities in the entranment of globally coupled oscillators, Phys Rev Lett. 74 (1995) 4341-4344
    • (1995) Phys Rev Lett. , vol.74 , pp. 4341-4344
    • Crawford, J.D.1
  • 15
    • 0002011105 scopus 로고    scopus 로고
    • Onset of cooperative entrainment in limit-cycle oscillators with uniform all-to-all interactions bifurcation of the order function
    • H Daido, Onset of cooperative entrainment in limit-cycle oscillators with uniform all-to-all interactions bifurcation of the order function, Physica D 91 (1996) 24-66
    • (1996) Physica D , vol.91 , pp. 24-66
    • Daido, H.1
  • 16
    • 0002192231 scopus 로고
    • Cooperative phenomena in coupled oscillator systems under external fields
    • H. Sakaguchi, Cooperative phenomena in coupled oscillator systems under external fields, Progr Theoret. Phys 79 (1988) 39-46
    • (1988) Progr Theoret. Phys , vol.79 , pp. 39-46
    • Sakaguchi, H.1
  • 17
    • 1542499302 scopus 로고
    • Stability of incoherence in a population of coupled oscillators
    • S.H Strogatz, R. Mirollo, Stability of incoherence in a population of coupled oscillators, J. Stat. Phys 63 (1991) 613-635.
    • (1991) J. Stat. Phys , vol.63 , pp. 613-635
    • Strogatz, S.H.1    Mirollo, R.2
  • 18
    • 4243765520 scopus 로고
    • Coupled nonlinear oscillators below the synchronization threshold relaxation by generalized Landau damping
    • S H Strogatz, R Mirollo, RC Matthews, Coupled nonlinear oscillators below the synchronization threshold relaxation by generalized Landau damping, Phys Rev. Lett. 68 (1992) 2730-2733.
    • (1992) Phys Rev. Lett. , vol.68 , pp. 2730-2733
    • Strogatz, S.H.1    Mirollo, R.2    Matthews, R.C.3
  • 19
    • 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 (1994) 1047-1084
    • (1994) J Stat. Phys. , vol.74 , pp. 1047-1084
    • Crawford, J.D.1
  • 20
    • 0000040998 scopus 로고
    • Introduction to bifurcation theory
    • J.D Crawford, Introduction to bifurcation theory, Rev Modern Phys 63 (1991) 991-1037.
    • (1991) Rev Modern Phys , vol.63 , pp. 991-1037
    • Crawford, J.D.1
  • 21
    • 0000950086 scopus 로고
    • Centre manifold theory in infinite dimensions
    • Springer, New York
    • A. Vanderbauwhede, G. Iooss, Centre manifold theory in infinite dimensions, in Dynamics Reported, vol 1, Springer, New York, 1992, pp. 125-163.
    • (1992) Dynamics Reported , vol.1 , pp. 125-163
    • Vanderbauwhede, A.1    Iooss, G.2
  • 22
    • 4244084028 scopus 로고
    • Universal trapping scaling on the unstable manifold of a collisionless electrostatic mode
    • J.D Crawford, Universal trapping scaling on the unstable manifold of a collisionless electrostatic mode, Phys Rev. Lett. 73 (1994) 656-659
    • (1994) Phys Rev. Lett. , vol.73 , pp. 656-659
    • Crawford, J.D.1
  • 23
    • 0007451224 scopus 로고
    • Amplitude equations for electrostatic waves, universal singular behavior in the limit of weak instability
    • J D. Crawford, Amplitude equations for electrostatic waves, universal singular behavior in the limit of weak instability, Phys Plasmas 2 (1995) 97-128
    • (1995) Phys Plasmas , vol.2 , pp. 97-128
    • Crawford, J.D.1
  • 24
    • 3743065083 scopus 로고    scopus 로고
    • Nonlinear saturation of electrostatic waves' mobile ions modify trapping scaling
    • J D Crawford, A. Jayaraman, Nonlinear saturation of electrostatic waves' mobile ions modify trapping scaling, Phys Rev Lett 77 (1996) 3549
    • (1996) Phys Rev Lett , vol.77 , pp. 3549
    • Crawford, J.D.1    Jayaraman, A.2
  • 25
    • 0001244972 scopus 로고
    • Stability of inviscid plane Couette flow
    • K Case, Stability of inviscid plane Couette flow, Phys Fluids 3 (1960) 143
    • (1960) Phys Fluids , vol.3 , pp. 143
    • Case, K.1
  • 26
    • 0014734772 scopus 로고
    • Role of Landau damping in crossed-field electron beams and inviscid shear flow
    • R.J Briggs, J.D. Daugherty, R H Levy, Role of Landau damping in crossed-field electron beams and inviscid shear flow, Phys Fluids 13 (1970) 421-432
    • (1970) Phys Fluids , vol.13 , pp. 421-432
    • Briggs, R.J.1    Daugherty, J.D.2    Levy, R.H.3
  • 29
    • 0001726136 scopus 로고
    • Oscillatory instability of solitary waves in a continuum model of lattice vibrations
    • R Pego, P. Smereka, M I. Weinstein, Oscillatory instability of solitary waves in a continuum model of lattice vibrations, Nonlinearity 8 (1995) 921-941.
    • (1995) Nonlinearity , vol.8 , pp. 921-941
    • Pego, R.1    Smereka, P.2    Weinstein, M.I.3
  • 30
    • 0030127191 scopus 로고    scopus 로고
    • Kinetic theory for bubbly flow I. collisionless case
    • G Russo, P. Smereka, Kinetic theory for bubbly flow I. collisionless case, SIAM J Appl Math 56 (1996)
    • (1996) SIAM J Appl Math , vol.56
    • Russo, G.1    Smereka, P.2
  • 31
    • 0010717259 scopus 로고
    • Critical conditions of macroscopic mutual entrainment in uniformly coupled limit-cycle oscillators
    • H Daido, Critical conditions of macroscopic mutual entrainment in uniformly coupled limit-cycle oscillators, Progr Theoret Phys 89 (1993) 929-934.
    • (1993) Progr Theoret Phys , vol.89 , pp. 929-934
    • Daido, H.1
  • 32
    • 0000058126 scopus 로고
    • Application of the method of spectral deformation to the Vlasov-Poisson system
    • J.D Crawford, P.D. Hislop, Application of the method of spectral deformation to the Vlasov-Poisson system, Ann Phys 189 (1989) 265-317.
    • (1989) Ann Phys , vol.189 , pp. 265-317
    • Crawford, J.D.1    Hislop, P.D.2
  • 34
    • 0000122907 scopus 로고
    • Order function and macroscopic mutual entrainment in uniformly coupled limit-cycle oscillators
    • H Daido, Order function and macroscopic mutual entrainment in uniformly coupled limit-cycle oscillators, Progr. Theoret Phys. 88 (1992) 1213-1218
    • (1992) Progr. Theoret Phys. , vol.88 , pp. 1213-1218
    • Daido, H.1
  • 35
    • 0001483954 scopus 로고
    • A solvable model of coupled limit-cycle oscillators exhibitig partial perfect synchrony and novel frequency spectra
    • H Daido, A solvable model of coupled limit-cycle oscillators exhibitig partial perfect synchrony and novel frequency spectra, Physica D 69 (1993) 394-403
    • (1993) Physica D , vol.69 , pp. 394-403
    • Daido, H.1
  • 36
    • 84957339412 scopus 로고
    • Noise-induced periodic behavior in the globally coupled complex Ginzburg-Landau equation
    • V Hakim, W -J. Rappel, Noise-induced periodic behavior in the globally coupled complex Ginzburg-Landau equation, Europhys Lett. 27 (1994) 637
    • (1994) Europhys Lett. , vol.27 , pp. 637
    • Hakim, V.1    Rappel, W.J.2
  • 39
    • 0000677291 scopus 로고
    • Stable nonequihbnum probability densities and phase transitions for mean-field models in the thermodynamic limit
    • L.L. Bonilla, Stable nonequihbnum probability densities and phase transitions for mean-field models in the thermodynamic limit, J Stat Phys. 46 (1987) 659.
    • (1987) J Stat Phys. , vol.46 , pp. 659
    • Bonilla, L.L.1
  • 40
    • 0030210666 scopus 로고    scopus 로고
    • McKean-Vlasov limit for interacting random processes in random media
    • P.D Pra, F den Hollander, McKean-Vlasov limit for interacting random processes in random media, J Stat. Phys 84 (1996) 735-772
    • (1996) J Stat. Phys , vol.84 , pp. 735-772
    • Pra, P.D.1    Den Hollander, F.2
  • 41
    • 0041339442 scopus 로고
    • Modelling complex systems stochastic processes, stochastic differential equations, and Fokker-Planck equations
    • L Nadel, D. Stein (Eds.), Addison-Wesley, New York
    • C.R Doering, Modelling complex systems stochastic processes, stochastic differential equations, and Fokker-Planck equations, in: L Nadel, D. Stein (Eds.), Lectures in Complex Systems, Addison-Wesley, New York, 1991, pp. 3-51.
    • (1991) Lectures in Complex Systems , pp. 3-51
    • Doering, C.R.1
  • 42
    • 0002429034 scopus 로고
    • Statistical mechanics of a nonlinear stochastic model
    • R C Desai, R. Zwanzig, Statistical mechanics of a nonlinear stochastic model, J Stat Phys 19 (1978) 1-24.
    • (1978) J Stat Phys , vol.19 , pp. 1-24
    • Desai, R.C.1    Zwanzig, R.2
  • 43
    • 34250144062 scopus 로고
    • Critical dynamics and fluctuations for a mean-field model of cooperative behavior
    • D.A. Dawson, Critical dynamics and fluctuations for a mean-field model of cooperative behavior, J Stat. Phys. 31 (1983) 29.
    • (1983) J Stat. Phys. , vol.31 , pp. 29
    • Dawson, D.A.1
  • 44
    • 34250080874 scopus 로고
    • Glassy synchronization in a population of coupled oscillators
    • L L Bonilla, C J Perez Vicente, J.M. Rubi, Glassy synchronization in a population of coupled oscillators, J. Stat Phys. 70 (1993) 921
    • (1993) J. Stat Phys. , vol.70 , pp. 921
    • Bonilla, L.L.1    Perez Vicente, C.J.2    Rubi, J.M.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.