메뉴 건너뛰기




Volumn 7, Issue 4, 2008, Pages 1445-1476

Stable synchrony in globally coupled integrate-and-fire oscillators

Author keywords

Concavity; Integrate and fire; Nonidentical oscillators; Stable synchrony

Indexed keywords

CONCAVITY; INITIAL CONDITIONS; INTEGRATE AND FIRES; NONIDENTICAL OSCILLATORS; STABLE SYNCHRONY; SUFFICIENT CONDITIONS;

EID: 70349643128     PISSN: None     EISSN: 15360040     Source Type: Journal    
DOI: 10.1137/070709220     Document Type: Article
Times cited : (7)

References (63)
  • 1
    • 0000411741 scopus 로고
    • A network of oscillators
    • L. F. Abbott, A network of oscillators, J. Phys. A, 23 (1990), pp. 3835-3859.
    • (1990) J. Phys. A , vol.23 , pp. 3835-3859
    • Abbott, L.F.1
  • 2
    • 22244458151 scopus 로고
    • Asynchronous states in networks of pulse-coupled oscillators
    • L. F. Abbott and C. van Vreeswijk, Asynchronous states in networks of pulse-coupled oscillators, Phys. Rev. E, 48 (1993), pp. 1483-1490.
    • (1993) Phys. Rev. E , vol.48 , pp. 1483-1490
    • Abbott, L.F.1    Van Vreeswijk, C.2
  • 4
    • 0034317183 scopus 로고    scopus 로고
    • Hierarchy and stability of partially synchronous oscillations of diffusively coupled dynamical systems
    • V. N. Belykh, I. V. Belykh, K. V. Nevidin, and M. Hasler, Hierarchy and stability of partially synchronous oscillations of diffusively coupled dynamical systems, Phys. Rev. E, 62 (2000), pp. 6332-6345.
    • (2000) Phys. Rev. E , vol.62 , pp. 6332-6345
    • Belykh, V.N.1    Belykh, I.V.2    Nevidin, K.V.3    Hasler, M.4
  • 6
    • 3042858242 scopus 로고    scopus 로고
    • Connection graph stability method for synchronized coupled chaotic systems
    • V. N. Belykh, I. V. Belykh, and M. Hasler, Connection graph stability method for synchronized coupled chaotic systems, Phys. D, 195 (2004), pp. 159-187.
    • (2004) Phys. D , vol.195 , pp. 159-187
    • Belykh, V.N.1    Belykh, I.V.2    Hasler, M.3
  • 7
    • 27144547553 scopus 로고    scopus 로고
    • Synchronization of bursting neurons: What matters in the network topology
    • I. Belykh, E. de Lange, and M. Hasler, Synchronization of bursting neurons: What matters in the network topology, Phys. Rev. Lett., 94 (2005), paper 188101.
    • (2005) Phys. Rev. Lett. , vol.94 , pp. 188101
    • Belykh, I.1    De Lange, E.2    Hasler, M.3
  • 8
    • 0000368785 scopus 로고
    • Pulse-coupled relaxation oscillators: From biological synchronization to self-organized criticality
    • S. Bottani, Pulse-coupled relaxation oscillators: From biological synchronization to self-organized criticality, Phys. Rev. Lett., 74 (1995), pp. 4189-4192.
    • (1995) Phys. Rev. Lett. , vol.74 , pp. 4189-4192
    • Bottani, S.1
  • 9
    • 0003794116 scopus 로고
    • The dynamics of two pulse-coupled relaxation oscillators
    • A. Brailove, The dynamics of two pulse-coupled relaxation oscillators, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 2 (1992), pp. 341-352.
    • (1992) Internat. J. Bifur. Chaos Appl. Sci. Engrg. , vol.2 , pp. 341-352
    • Brailove, A.1
  • 10
    • 0001068180 scopus 로고    scopus 로고
    • Synchrony in an array of integrate-and-fire neurons with dendritic structure
    • P. C. Bressloff and S. Coombes, Synchrony in an array of integrate-and-fire neurons with dendritic structure, Phys. Rev. Lett., 78 (1997), pp. 4665-4668.
    • (1997) Phys. Rev. Lett. , vol.78 , pp. 4665-4668
    • Bressloff, P.C.1    Coombes, S.2
  • 11
    • 0000624276 scopus 로고    scopus 로고
    • Desynchronization, mode locking, and bursting in strongly coupled integrate-and-fire oscillators
    • P. C. Bressloff and S. Coombes, Desynchronization, mode locking, and bursting in strongly coupled integrate-and-fire oscillators, Phys. Rev. Lett., 81 (1998), pp. 2168-2171.
    • (1998) Phys. Rev. Lett. , vol.81 , pp. 2168-2171
    • Bressloff, P.C.1    Coombes, S.2
  • 12
    • 0033076746 scopus 로고    scopus 로고
    • Symmetry and phase-locking in a ring of pulse-coupled oscillators with distributed delays
    • P. C. Bressloff and S. Coombes, Symmetry and phase-locking in a ring of pulse-coupled oscillators with distributed delays, Phys. D, 126 (1999), pp. 99-122.
    • (1999) Phys. D , vol.126 , pp. 99-122
    • Bressloff, P.C.1    Coombes, S.2
  • 13
    • 0024165008 scopus 로고
    • Synchronous rhythmic flashing of fireflies. II
    • J. Buck, Synchronous rhythmic flashing of fireflies. II, Quart. Rev. Biol., 63 (1988), pp. 265-289.
    • (1988) Quart. Rev. Biol. , vol.63 , pp. 265-289
    • Buck, J.1
  • 14
    • 0001380222 scopus 로고    scopus 로고
    • Phase-locking in weakly heterogeneous neuronal networks
    • C. Chow, Phase-locking in weakly heterogeneous neuronal networks, Phys. D, 118 (1998), pp. 343-370.
    • (1998) Phys. D , vol.118 , pp. 343-370
    • Chow, C.1
  • 15
    • 0000945656 scopus 로고
    • Lower critical dimension for populations of oscillators with randomly distributed frequencies: A renormalization-group analysis
    • H. Daido, Lower critical dimension for populations of oscillators with randomly distributed frequencies: A renormalization-group analysis, Phys. Rev. Lett., 61 (1988), pp. 231-234.
    • (1988) Phys. Rev. Lett. , vol.61 , pp. 231-234
    • Daido, H.1
  • 16
    • 0009222930 scopus 로고
    • Intrinsic fluctuation and its critical scaling in a class of populations of oscillators with distributed frequencies
    • H. Daido, Intrinsic fluctuation and its critical scaling in a class of populations of oscillators with distributed frequencies, Progr. Theoret. Phys., 81 (1989), pp. 727-731.
    • (1989) Progr. Theoret. Phys. , vol.81 , pp. 727-731
    • Daido, H.1
  • 17
    • 29444442092 scopus 로고
    • Intrinsic fluctuations and a phase transition in a class of large populations of interacting oscillators
    • H. Daido, Intrinsic fluctuations and a phase transition in a class of large populations of interacting oscillators, J. Statist. Phys., 60 (1990), pp. 753-800.
    • (1990) J. Statist. Phys. , vol.60 , pp. 753-800
    • Daido, H.1
  • 18
    • 0000747853 scopus 로고
    • Frequency plateaus in a chain of weakly coupled oscillators
    • G. B. Ermentrout and N. Kopell, Frequency plateaus in a chain of weakly coupled oscillators, SIAM J. Math. Anal., 15 (1984), pp. 215-237.
    • (1984) SIAM J. Math. Anal. , vol.15 , pp. 215-237
    • Ermentrout, G.B.1    Kopell, N.2
  • 19
    • 0021876815 scopus 로고
    • Synchronization in a pool of mutually coupled oscillators with random frequencies
    • G. B. Ermentrout, Synchronization in a pool of mutually coupled oscillators with random frequencies, J. Math. Biol., 22 (1985), pp. 1-9.
    • (1985) J. Math. Biol. , vol.22 , pp. 1-9
    • Ermentrout, G.B.1
  • 20
    • 5944222448 scopus 로고
    • An adaptive model for synchrony in the firefly Pteroptyx malaccae
    • G. Ermentrout, An adaptive model for synchrony in the firefly Pteroptyx malaccae, J. Math. Biol., 29 (1991), pp. 571-585.
    • (1991) J. Math. Biol. , vol.29 , pp. 571-585
    • Ermentrout, G.1
  • 21
    • 24244469769 scopus 로고    scopus 로고
    • Delay-induced multistable synchronization of biological oscillators
    • U. Ernst, K. Pawelzik, and T. Geisel, Delay-induced multistable synchronization of biological oscillators, Phys. Rev. E, 57 (1998), pp. 2150-2162.
    • (1998) Phys. Rev. E , vol.57 , pp. 2150-2162
    • Ernst, U.1    Pawelzik, K.2    Geisel, T.3
  • 24
    • 0027357806 scopus 로고
    • A biologically motivated and analytically soluble model of collective oscillations in the cortex: I. Theory of weak locking
    • W. Gerstner, R. Ritz, and J. L. van Hemmen, A biologically motivated and analytically soluble model of collective oscillations in the cortex: I. Theory of weak locking, Biolog. Cybernet., 68 (1993), pp. 363-374.
    • (1993) Biolog. Cybernet. , vol.68 , pp. 363-374
    • Gerstner, W.1    Ritz, R.2    Van Hemmen, J.L.3
  • 25
    • 0037087313 scopus 로고    scopus 로고
    • Synchrony, stability, and firing patterns in pulse-coupled oscillators
    • P. Goel and B. Ermentrout, Synchrony, stability, and firing patterns in pulse-coupled oscillators, Phys. D, 163 (2002), pp. 191-216.
    • (2002) Phys. D , vol.163 , pp. 191-216
    • Goel, P.1    Ermentrout, B.2
  • 26
    • 0029258143 scopus 로고
    • Synchrony in excitatory neural networks
    • D. Hansel, G. Mato, and C. Meunier, Synchrony in excitatory neural networks, Neural Computation, 7 (1995), pp. 307-337.
    • (1995) Neural Computation , vol.7 , pp. 307-337
    • Hansel, D.1    Mato, G.2    Meunier, C.3
  • 27
    • 0035971275 scopus 로고    scopus 로고
    • Existence and stability of persistent states in large neuronal networks
    • D. Hansel and G. Mato, Existence and stability of persistent states in large neuronal networks, Phys. Rev. Lett., 86 (2001), pp. 4175-4178.
    • (2001) Phys. Rev. Lett. , vol.86 , pp. 4175-4178
    • Hansel, D.1    Mato, G.2
  • 28
    • 0032667738 scopus 로고    scopus 로고
    • Class 1 neural excitability, conventional synapses, weakly connected networks, and mathematical foundations of pulse-coupled models
    • E. Izhikevich, Class 1 neural excitability, conventional synapses, weakly connected networks, and mathematical foundations of pulse-coupled models, IEEE Trans. Neural Networks, 10 (1999), pp. 499-507.
    • (1999) IEEE Trans. Neural Networks , vol.10 , pp. 499-507
    • Izhikevich, E.1
  • 29
    • 0021286743 scopus 로고
    • Mutual entrainment and electrical coupling as mechanisms for synchronous firing of rabbit sinoatrial pacemaker cells
    • J. Jalife, Mutual entrainment and electrical coupling as mechanisms for synchronous firing of rabbit sinoatrial pacemaker cells, J. Physiol., 356 (1984), pp. 221-243.
    • (1984) J. Physiol. , vol.356 , pp. 221-243
    • Jalife, J.1
  • 30
    • 34848874143 scopus 로고    scopus 로고
    • Global synchronization in lattices of coupled chaotic systems
    • J. Juang, C. L. Li, and Y. H. Liang, Global synchronization in lattices of coupled chaotic systems, Chaos, 17 (2007), paper 033111.
    • (2007) Chaos , vol.17 , pp. 033111
    • Juang, J.1    Li, C.L.2    Liang, Y.H.3
  • 31
    • 55849103482 scopus 로고    scopus 로고
    • Synchronous chaos in coupled map lattices with general connectivity topology
    • J. Juang and Y.-H. Liang, Synchronous chaos in coupled map lattices with general connectivity topology, SIAM J. Appl. Dyn. Syst., 7 (2008), pp. 755-765.
    • (2008) SIAM J. Appl. Dyn. Syst. , vol.7 , pp. 755-765
    • Juang, J.1    Liang, Y.-H.2
  • 32
    • 78649638623 scopus 로고    scopus 로고
    • Mechanisms of phase-locking and frequency control in pairs of coupled neural oscillators
    • Towards Applications, B. Fiedler, G. Iooss, and N. Kopell, eds., Elsevier, New York
    • N. Kopell and G. B. Ermentrout, Mechanisms of phase-locking and frequency control in pairs of coupled neural oscillators, in Handbook of Dynamical Systems, Vol. 3, Towards Applications, B. Fiedler, G. Iooss, and N. Kopell, eds., Elsevier, New York, 2000.
    • (2000) Handbook of Dynamical Systems , vol.3
    • Kopell, N.1    Ermentrout, G.B.2
  • 35
    • 0001551665 scopus 로고
    • Statistical macrodynamics of large dynamical systems. Case of a phase transition in oscillator communities
    • Y. Kuramoto and I. Nishikawa, Statistical macrodynamics of large dynamical systems. Case of a phase transition in oscillator communities, J. Statist. Phys., 49 (1987), pp. 596-605.
    • (1987) J. Statist. Phys. , vol.49 , pp. 596-605
    • Kuramoto, Y.1    Nishikawa, I.2
  • 36
    • 44949272252 scopus 로고
    • Collective synchronization of pulse-coupled oscillators and excitable units
    • Y. Kuramoto, Collective synchronization of pulse-coupled oscillators and excitable units, Phys. D, 50 (1991), pp. 15-30.
    • (1991) Phys. D , vol.50 , pp. 15-30
    • Kuramoto, Y.1
  • 37
    • 0942299306 scopus 로고    scopus 로고
    • Chaos synchronization of general complex dynamical networks
    • J. Lü, X. Yu, and G. Chen, Chaos synchronization of general complex dynamical networks, Phys. A, 334 (2004), pp. 281-302.
    • (2004) Phys. A , vol.334 , pp. 281-302
    • Lü, J.1    Yu, X.2    Chen, G.3
  • 38
    • 21344466279 scopus 로고    scopus 로고
    • A time-varying complex dynamical network model and its controlling synchronization criteria
    • J. Lü, X. Yu, and G. Chen, A time-varying complex dynamical network model and its controlling synchronization criteria, IEEE Trans. Automat. Control, 50 (2005), pp. 841-846.
    • (2005) IEEE Trans. Automat. Control , vol.50 , pp. 841-846
    • Lü, J.1    Yu, X.2    Chen, G.3
  • 39
    • 0000918668 scopus 로고
    • Phase diagram for the collective behavior of limit-cycle oscillators
    • P. C. Matthews and S. H. Strogatz, Phase diagram for the collective behavior of limit-cycle oscillators, Phys. Rev. Lett., 65 (1990), pp. 1701-1704.
    • (1990) Phys. Rev. Lett. , vol.65 , pp. 1701-1704
    • Matthews, P.C.1    Strogatz, S.H.2
  • 40
    • 0023204733 scopus 로고
    • Mechanisms of sinoatrial pacemaker synchronization: A new hypothesis
    • D. C. Michaels, E. P. Matyas, and J. Jalife, Mechanisms of sinoatrial pacemaker synchronization: A new hypothesis, Circulation Res., 61 (1987), pp. 704-714.
    • (1987) Circulation Res , vol.61 , pp. 704-714
    • Michaels, D.C.1    Matyas, E.P.2    Jalife, J.3
  • 41
    • 0025567093 scopus 로고
    • Synchronization of pulse-coupled biological oscillators
    • R. E. Mirollo and S. H. Strogatz, Synchronization of pulse-coupled biological oscillators, SIAM J. Appl. Math., 50 (1990), pp. 1645-1662.
    • (1990) SIAM J. Appl. Math. , vol.50 , pp. 1645-1662
    • Mirollo, R.E.1    Strogatz, S.H.2
  • 42
    • 0041707963 scopus 로고    scopus 로고
    • Heterogeneity in oscillator networks: Are smaller worlds easier to synchronize?
    • T. Nishikawa, A. E. Motter, Y. C. Lai, and F. C. Hoppensteadt, Heterogeneity in oscillator networks: Are smaller worlds easier to synchronize?, Phys. Rev. Lett., 91 (2003), paper 014101.
    • (2003) Phys. Rev. Lett. , vol.91 , pp. 014101
    • Nishikawa, T.1    Motter, A.E.2    Lai, Y.C.3    Hoppensteadt, F.C.4
  • 43
    • 0003913214 scopus 로고
    • Courant Institute of Mathematical Sciences, New York University, New York
    • C. S. Peskin, Mathematical Aspects of Heart Physiology, Courant Institute of Mathematical Sciences, New York University, New York, 1975.
    • (1975) Mathematical Aspects of Heart Physiology
    • Peskin, C.S.1
  • 45
    • 0034150797 scopus 로고    scopus 로고
    • Geometric analysis of population rhythms in synaptically coupled neuronal networks
    • J. Rubin and D. Terman, Geometric analysis of population rhythms in synaptically coupled neuronal networks, Neural Computation, 12 (2000), pp. 597-645.
    • (2000) Neural Computation , vol.12 , pp. 597-645
    • Rubin, J.1    Terman, D.2
  • 46
    • 0034576375 scopus 로고    scopus 로고
    • Analysis of clustered firing patterns in synaptically coupled networks of oscillators
    • J. Rubin and D. Terman, Analysis of clustered firing patterns in synaptically coupled networks of oscillators, J. Math. Biol., 41 (2000), pp. 513-545.
    • (2000) J. Math. Biol. , vol.41 , pp. 513-545
    • Rubin, J.1    Terman, D.2
  • 47
    • 3042676195 scopus 로고    scopus 로고
    • Synchronized activity and loss of synchrony among heterogeneous conditional oscillators
    • J. Rubin and D. Terman, Synchronized activity and loss of synchrony among heterogeneous conditional oscillators, SIAM J. Appl. Dyn. Syst., 1 (2002), pp. 146-174.
    • (2002) SIAM J. Appl. Dyn. Syst. , vol.1 , pp. 146-174
    • Rubin, J.1    Terman, D.2
  • 48
    • 0023791327 scopus 로고
    • Emergence of organized bursting in clusters of pancreatic beta-cells by channel sharing
    • A. Sherman, J. Rinzel, and J. Keizer, Emergence of organized bursting in clusters of pancreatic beta-cells by channel sharing, Biophys. J., 54 (1988), pp. 411-425.
    • (1988) Biophys. J. , vol.54 , pp. 411-425
    • Sherman, A.1    Rinzel, J.2    Keizer, J.3
  • 52
    • 0000559957 scopus 로고
    • Phase-locking and critical phenomena in lattices of coupled nonlinear oscillators with random intrinsic frequencies
    • S. H. Strogatz and R. E. Mirollo, Phase-locking and critical phenomena in lattices of coupled nonlinear oscillators with random intrinsic frequencies, Phys. D, 31 (1988), pp. 143-168.
    • (1988) Phys. D , vol.31 , pp. 143-168
    • Strogatz, S.H.1    Mirollo, R.E.2
  • 53
    • 36149036075 scopus 로고
    • Collective synchronisation in lattices of nonlinear oscillators with randomness
    • S. H. Strogatz and R. E. Mirollo, Collective synchronisation in lattices of nonlinear oscillators with randomness, J. Phys. A, 21 (1988), pp. L699-L705.
    • (1988) J. Phys. A , vol.21
    • Strogatz, S.H.1    Mirollo, R.E.2
  • 54
    • 0000821114 scopus 로고    scopus 로고
    • Dynamics of two mutually coupled slow inhibitory neurons
    • D. Terman, N. Kopell, and A. Bose, Dynamics of two mutually coupled slow inhibitory neurons, Phys. D, 117 (1998), pp. 241-275.
    • (1998) Phys. D , vol.117 , pp. 241-275
    • Terman, D.1    Kopell, N.2    Bose, A.3
  • 55
    • 0017172994 scopus 로고
    • A theory of synchronization of heart pace-maker cells
    • V. Torre, A theory of synchronization of heart pace-maker cells, J. Theoret. Biol., 61 (1976), pp. 55-71.
    • (1976) J. Theoret. Biol. , vol.61 , pp. 55-71
    • Torre, V.1
  • 56
    • 0000094836 scopus 로고
    • Pattern of synchrony in inhomogeneous networks of oscillators with pulse interactions
    • M. Tsodyks, I. Mitkov, and H. Sompolinsky, Pattern of synchrony in inhomogeneous networks of oscillators with pulse interactions, Phys. Rev. Lett., 71 (1993), pp. 1280-1283.
    • (1993) Phys. Rev. Lett. , vol.71 , pp. 1280-1283
    • Tsodyks, M.1    Mitkov, I.2    Sompolinsky, H.3
  • 57
    • 0034844437 scopus 로고    scopus 로고
    • Similar nonleaky integrate-and-fire neurons with instantaneous couplings always synchronize
    • R. Urbanczik and W. Senn, Similar nonleaky integrate-and-fire neurons with instantaneous couplings always synchronize, SIAM J. Appl. Math., 61 (2000), pp. 1143-1155.
    • (2000) SIAM J. Appl. Math. , vol.61 , pp. 1143-1155
    • Urbanczik, R.1    Senn, W.2
  • 58
    • 0028679412 scopus 로고
    • When inhibition not excitation synchronizes neural firing
    • C. van Vreeswijk, L. Abbott, and G. Ermentrout, When inhibition not excitation synchronizes neural firing, J. Comp. Neurosci., 1 (1994), pp. 313-321.
    • (1994) J. Comp. Neurosci. , vol.1 , pp. 313-321
    • Van Vreeswijk, C.1    Abbott, L.2    Ermentrout, G.3
  • 59
    • 0000563446 scopus 로고    scopus 로고
    • Partially synchronized states in networks of pulse-coupled neurons
    • C. van Vreeswijk, Partially synchronized states in networks of pulse-coupled neurons, Phys. Rev. E, 54 (1996), pp. 5522-5537.
    • (1996) Phys. Rev. E , vol.54 , pp. 5522-5537
    • Van Vreeswijk, C.1
  • 60
    • 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), pp. 15-42.
    • (1967) J. Theoret. Biol. , vol.16 , pp. 15-42
    • Winfree, A.T.1
  • 62
    • 52149119375 scopus 로고    scopus 로고
    • Synchronization in coupled chaotic circuits and systems
    • World Scientific, Singapore
    • C. W. Wu, Synchronization in Coupled Chaotic Circuits and Systems, World Sci. Ser. Nonlinear Sci. Ser. A Monogr. Treatises 41, World Scientific, Singapore, 2002.
    • (2002) World Sci. Ser. Nonlinear Sci. Ser. A Monogr. Treatises , vol.41
    • Wu, C.W.1
  • 63
    • 0000307688 scopus 로고    scopus 로고
    • Chaos synchronization in coupled chaotic oscillators with multiple positive Lyapunov exponents
    • J. Yang, G. Hu, and J. Xiao, Chaos synchronization in coupled chaotic oscillators with multiple positive Lyapunov exponents, Phys. Rev. Lett., 80 (2003), pp. 496-499.
    • (2003) Phys. Rev. Lett. , vol.80 , pp. 496-499
    • Yang, J.1    Hu, G.2    Xiao, J.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.