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Volumn 16, Issue 3, 2006, Pages 201-231

Winding numbers and average frequencies in phase oscillator networks

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EID: 84867939262     PISSN: 09388974     EISSN: 14321467     Source Type: Journal    
DOI: 10.1007/s00332-005-0696-3     Document Type: Review
Times cited : (20)

References (32)
  • 1
    • 42749100240 scopus 로고    scopus 로고
    • Encoding via conjugate symmetries of slow oscillations for globally coupled oscillators
    • P. Ashwin and J. Borresen. Encoding via conjugate symmetries of slow oscillations for globally coupled oscillators. Phys. Rev. E 70 (2004) 026203.
    • (2004) Phys. Rev. e , vol.70 , pp. 026203
    • Ashwin, P.1    Borresen, J.2
  • 2
    • 84867996498 scopus 로고    scopus 로고
    • P. Ashwin, O. Burilko, Y. Maistrenko, and O. Popovych (in preparation)
    • P. Ashwin, O. Burilko, Y. Maistrenko, and O. Popovych (in preparation).
  • 3
    • 34249831818 scopus 로고
    • The dynamics of n weakly coupled identical oscillators
    • P. Ashwin and J. W. Swift. The dynamics of n weakly coupled identical oscillators. J. Nonlinear Sci. 2(1) (1992) 69-108.
    • (1992) J. Nonlinear Sci. , vol.2 , Issue.1 , pp. 69-108
    • Ashwin, P.1    Swift, J.W.2
  • 4
    • 1542351229 scopus 로고    scopus 로고
    • On the phase reduction and response dynamics of neural oscillator populations
    • DOI 10.1162/089976604322860668
    • E. Brown, J. Moehlis, and P. Holmes. On the phase reduction and response dynamics of neural oscillator populations. Neural Comp. 16 (2004) 673-715. (Pubitemid 38318129)
    • (2004) Neural Computation , vol.16 , Issue.4 , pp. 673-715
    • Brown, E.1    Moehlis, J.2    Holmes, P.3
  • 5
    • 0033473374 scopus 로고    scopus 로고
    • On the continuation of an invariant torus in a family with rapid oscillations
    • PII S0036141098338740
    • C. Chicone and W. Liu. On the continuation of an invariant torus in a family with rapid oscillations. SIAM J. Math. Anal. 31(2) (1999-2000) 386-415. (Pubitemid 129341660)
    • (1999) SIAM Journal on Mathematical Analysis , vol.31 , Issue.2 , pp. 386-415
    • Chicone, C.1    Liu, W.2
  • 7
    • 0030195232 scopus 로고    scopus 로고
    • Type i membranes, phase resetting curves, and synchrony
    • G. B. Ermentrout. Type I membranes, phase resetting curves, and synchrony. Neural Comp. 8 (1996) 979-1001.
    • (1996) Neural Comp. , vol.8 , pp. 979-1001
    • Ermentrout, G.B.1
  • 9
    • 0001356311 scopus 로고
    • Persistence and smoothness of invariant manifolds for flows
    • N. Fenichel. Persistence and smoothness of invariant manifolds for flows. Indiana Univ. Math. J. 21 (1971-1972) 193-226.
    • (1971) Indiana Univ. Math. J. , vol.21 , pp. 193-226
    • Fenichel, N.1
  • 15
    • 11144319940 scopus 로고    scopus 로고
    • Patterns of synchrony in coupled cell networks with multiple arrows
    • DOI 10.1137/040612634
    • M. Golubitsky, I. N. Stewart, and A. T̈or̈ok. Patterns of synchrony in coupled cell networks with multiple arrows. SIAM J. Appl. Dynam. Sys. 4(1) (2005) 78-100. (Pubitemid 43385187)
    • (2005) SIAM Journal on Applied Dynamical Systems , vol.4 , Issue.1 , pp. 78-100
    • Golubitsky, M.1    Steward, I.2    Torok, A.3
  • 16
    • 0016314153 scopus 로고
    • Isochrons and phaseless sets
    • J. Guckenheimer. Isochrons and phaseless sets. J. Math. Biol. 1 (1975) 259-273.
    • (1975) J. Math. Biol. , vol.1 , pp. 259-273
    • Guckenheimer, J.1
  • 18
    • 3242768234 scopus 로고    scopus 로고
    • Spike-timing dynamics of neuronal groups
    • DOI 10.1093/cercor/bhh053
    • E. Izhikevich, J. Gally, and G. Edelman. Spike-timing Dynamics of Neuronal Groups. Cerebral Cortex. 14(8) (2004) 933-944. (Pubitemid 38971467)
    • (2004) Cerebral Cortex , vol.14 , Issue.8 , pp. 933-944
    • Izhikevich, E.M.1    Gally, J.A.2    Edelman, G.M.3
  • 20
    • 0000747853 scopus 로고
    • Frequency plateaus in a chain of weakly coupled oscillators i
    • N. Kopell and G. B. Ermentrout. Frequency plateaus in a chain of weakly coupled oscillators, I. SIAM J. Math. Anal. 15 (1984) 215-237.
    • (1984) SIAM J. Math. Anal. , vol.15 , pp. 215-237
    • Kopell, N.1    Ermentrout, G.B.2
  • 21
    • 0031115637 scopus 로고    scopus 로고
    • Phase- and center-manifold reductions for large populations of coupled oscillators with application to non-locally coupled systems
    • Y. Kuramoto. Phase-and center-manifold reductions for large populations of coupled oscillators with application to non-locally coupled systems. Int. J. Bif. Chaos 7 (1997) 789-805. (Pubitemid 127338618)
    • (1997) International Journal of Bifurcation and Chaos in Applied Sciences and Engineering , vol.7 , Issue.4 , pp. 789-805
    • Kuramoto, Y.1
  • 22
    • 0000238781 scopus 로고
    • Small periodic perturbations of an autonomous system with a stable orbit
    • N. Levinson. Small periodic perturbations of an autonomous system with a stable orbit. Ann. Math. 52 (1950) 727-738.
    • (1950) Ann. Math. , vol.52 , pp. 727-738
    • Levinson, N.1
  • 23
    • 0038701723 scopus 로고    scopus 로고
    • Dynamics of spiking neurons connected by both inhibitory and electrical coupling
    • DOI 10.1023/A:1023265027714
    • T. Lewis and J. Rinzel. Dynamics of spiking neurons connected by both inhibitory and electrical coupling. J. Comp. Neurosci. 14 (2003) 283-309. (Pubitemid 36596481)
    • (2003) Journal of Computational Neuroscience , vol.14 , Issue.3 , pp. 283-309
    • Lewis, T.J.1    Rinzel, J.2
  • 24
    • 0036834701 scopus 로고    scopus 로고
    • Real-time computing without stable states: A new framework for neural computation based on perturbations
    • W. Maass, T. Natschlager, and H. Markram. Real-Time Computing without Stable States: ANewFramework for Neural Computation Based on Perturbations. Neural Comp. 14 (2002) 2531-2560.
    • (2002) Neural Comp. , vol.14 , pp. 2531-2560
    • Maass, W.1    Natschlager, T.2    Markram, H.3
  • 26
    • 13744259954 scopus 로고    scopus 로고
    • Similar network activity from disparate circuit parameters
    • DOI 10.1038/nn1352
    • A. A. Prinz, D. Bucher, and E. Marder. Similar network activity from disparate circuit parameters. Nature Neurosci. 7 (2004) 1345-1352. (Pubitemid 41057757)
    • (2004) Nature Neuroscience , vol.7 , Issue.12 , pp. 1345-1352
    • Prinz, A.A.1    Bucher, D.2    Marder, E.3
  • 27
    • 0033860923 scopus 로고    scopus 로고
    • Competitive hebbian learning through spiketiming-dependent synaptic plasticity
    • S. Song, K. D. Miller, and L. F. Abbott. Competitive Hebbian learning through spiketiming-dependent synaptic plasticity. Nature Neurosci. 3 (2000) 919-926.
    • (2000) Nature Neurosci , vol.3 , pp. 919-926
    • Song, S.1    Miller, K.D.2    Abbott, L.F.3
  • 28
    • 3042534417 scopus 로고    scopus 로고
    • Symmetry groupoids and patterns of synchrony in coupled cell networks
    • DOI 10.1137/S1111111103419896
    • I. Stewart, M. Golubitsky, and M. Pivato. Symmetry groupoids and patterns of synchrony in coupled cell networks. SIAM J. Appl. Dynam. Sys. 2(4) (2003) 609-646. (Pubitemid 38818590)
    • (2003) SIAM Journal on Applied Dynamical Systems , vol.2 , Issue.4 , pp. 609-646
    • Stewart, I.1    Golubitsky, M.2    Pivato, M.3
  • 30
    • 4243284341 scopus 로고
    • Attractor crowding in oscillator arrays
    • K. Wiesenfeld and P. Hadley. Attractor crowding in oscillator arrays. Phys. Rev. Lett. 62 (1989) 1335-1338.
    • (1989) Phys. Rev. Lett. , vol.62 , pp. 1335-1338
    • Wiesenfeld, K.1    Hadley, P.2
  • 32
    • 84868002067 scopus 로고    scopus 로고
    • Special edition of Neuron 7-9 (September 1999)
    • Special edition of Neuron 7-9 (September 1999).


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