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Volumn 3, Issue 1, 2013, Pages 1-22

Phase-amplitude descriptions of neural oscillator models

Author keywords

Chaos; Non weak coupling; Oscillator; Phase amplitude

Indexed keywords

ARTICLE; CONDUCTANCE; NERVE CELL; NEUROSCIENCE; OSCILLATOR; PRIORITY JOURNAL; STIMULATION;

EID: 84881362110     PISSN: None     EISSN: 21908567     Source Type: Journal    
DOI: 10.1186/2190-8567-3-2     Document Type: Article
Times cited : (93)

References (37)
  • 2
    • 0016314153 scopus 로고
    • Isochrons and phaseless sets
    • Guckenheimer J: Isochrons and phaseless sets. J Math Biol 1975, 1:259-273.
    • (1975) J Math Biol , vol.1 , pp. 259-273
    • Guckenheimer, J.1
  • 4
    • 84990585743 scopus 로고
    • Symmetry and phaselocking in chains of weakly coupled oscillators
    • Kopell N, Ermentrout GB: Symmetry and phaselocking in chains of weakly coupled oscillators. Commun Pure Appl Math 1986, 39:623-660.
    • (1986) Commun Pure Appl Math , vol.39 , pp. 623-660
    • Kopell, N.1    Ermentrout, G.B.2
  • 5
    • 0019443177 scopus 로고
    • n:M phase-locking of weakly coupled oscillators
    • Ermentrout GB: n:m phase-locking of weakly coupled oscillators. J Math Biol 1981, 12:327-342.
    • (1981) J Math Biol , vol.12 , pp. 327-342
    • Ermentrout, G.B.1
  • 9
    • 85013998658 scopus 로고    scopus 로고
    • A computational and geometric approach to phase resetting curves and surfaces
    • Guillamon A, Huguet G: A computational and geometric approach to phase resetting curves and surfaces. SIAM J Appl Dyn Syst 2009, 8(3):1005-1042.
    • (2009) SIAM J Appl Dyn Syst , vol.8 , Issue.3 , pp. 1005-1042
    • Guillamon, A.1    Huguet, G.2
  • 10
    • 79251562186 scopus 로고    scopus 로고
    • A continuation method for computing global isochrons
    • Osinga HM, Moehlis J: A continuation method for computing global isochrons. SIAM J Appl Dyn Syst 2010, 9(4):1201-1228.
    • (2010) SIAM J Appl Dyn Syst , vol.9 , Issue.4 , pp. 1201-1228
    • Osinga, H.M.1    Moehlis, J.2
  • 11
    • 84866924926 scopus 로고    scopus 로고
    • On the use of Fourier averages to compute the global isochrons of (quasi)periodic dynamics
    • Mauroy A, Mezic I: On the use of Fourier averages to compute the global isochrons of (quasi)periodic dynamics. Chaos 2012, 22(3):033112.
    • (2012) Chaos , vol.22 , Issue.3 , pp. 033112
    • Mauroy, A.1    Mezic, I.2
  • 12
    • 1542351229 scopus 로고    scopus 로고
    • On the phase reduction and response dynamics of neural oscillator populations
    • Brown E, Moehlis J, Holmes P: On the phase reduction and response dynamics of neural oscillator populations. Neural Comput 2004, 16:673-715.
    • (2004) Neural Comput , vol.16 , pp. 673-715
    • Brown, E.1    Moehlis, J.2    Holmes, P.3
  • 14
    • 65549117124 scopus 로고    scopus 로고
    • Phase-resetting curves determine synchronization, phase locking, and clustering in networks of neural oscillators
    • Achuthan S, Canavier CC: Phase-resetting curves determine synchronization, phase locking, and clustering in networks of neural oscillators. J Neurosci 2009, 29(16):5218-5233.
    • (2009) J Neurosci , vol.29 , Issue.16 , pp. 5218-5233
    • Achuthan, S.1    Canavier, C.C.2
  • 15
    • 77957586622 scopus 로고    scopus 로고
    • Phase reduction of stochastic limit-cycle oscillators
    • New York: Wiley
    • Yoshimura K: Phase reduction of stochastic limit-cycle oscillators. In Reviews of Nonlinear Dynamics and Complexity. Volume 3. New York: Wiley; 2010:59-90.
    • (2010) Reviews of Nonlinear Dynamics and Complexity , vol.3 , pp. 59-90
    • Yoshimura, K.1
  • 16
    • 84871965667 scopus 로고    scopus 로고
    • Limitations of perturbative techniques in the analysis of rhythms and oscillations
    • Lin KK, Wedgwood KCA, Coombes S, Young LS: Limitations of perturbative techniques in the analysis of rhythms and oscillations. J Math Biol 2013, 66:139-161.
    • (2013) J Math Biol , vol.66 , pp. 139-161
    • Lin, K.K.1    Wedgwood, K.C.A.2    Coombes, S.3    Young, L.S.4
  • 17
    • 77954872218 scopus 로고    scopus 로고
    • Quadratic approximations for the isochrons of oscillators: A general theory, advanced numerical methods and accurate phase computations
    • Demir A, Suvak O: Quadratic approximations for the isochrons of oscillators: a general theory, advanced numerical methods and accurate phase computations. IEEE Trans Comput-Aided Des Integr Circuits Syst 2010, 29:1215-1228.
    • (2010) IEEE Trans Comput-Aided Des Integr Circuits Syst , vol.29 , pp. 1215-1228
    • Demir, A.1    Suvak, O.2
  • 18
    • 77949276956 scopus 로고    scopus 로고
    • Synchronization of coupled stochastic limit cycle oscillators
    • Medvedev GS: Synchronization of coupled stochastic limit cycle oscillators. Phys Lett A 2010, 374:1712-1720.
    • (2010) Phys Lett A , vol.374 , pp. 1712-1720
    • Medvedev, G.S.1
  • 19
    • 0012107296 scopus 로고
    • On systems of ordinary differential equations
    • Princeton: Princeton University Press, Annals of Mathematical Studies
    • Diliberto SP: On systems of ordinary differential equations. In Contributions to the Theory of Nonlinear Oscillations. Princeton: Princeton University Press; 1950:1-38. [Annals of Mathematical Studies, vol. 20.]
    • (1950) Contributions to The Theory of Nonlinear Oscillations , vol.20 , pp. 1-38
    • Diliberto, S.P.1
  • 21
    • 0025388272 scopus 로고
    • Oscillator death in systems of coupled neural oscillators
    • Ermentrout GB, Kopell N: Oscillator death in systems of coupled neural oscillators. SIAM J Appl Math 1990, 50:125-146.
    • (1990) SIAM J Appl Math , vol.50 , pp. 125-146
    • Ermentrout, G.B.1    Kopell, N.2
  • 22
    • 77949659246 scopus 로고    scopus 로고
    • From limit cycles to strange attractors
    • Ott W, Stenlund M: From limit cycles to strange attractors. Commun Math Phys 2010, 296:215-249.
    • (2010) Commun Math Phys , vol.296 , pp. 215-249
    • Ott, W.1    Stenlund, M.2
  • 23
    • 0019405994 scopus 로고
    • Voltage oscillations in the barnacle giant muscle fiber
    • Morris C, Lecar H: Voltage oscillations in the barnacle giant muscle fiber. Biophys J 1981, 35:193-213.
    • (1981) Biophys J , vol.35 , pp. 193-213
    • Morris, C.1    Lecar, H.2
  • 24
    • 0002453062 scopus 로고
    • Analysis of neural excitability and oscillations
    • 1st edition. Cambridge: MIT Press
    • Rinzel J, Ermentrout GB: Analysis of neural excitability and oscillations. In Methods in Neuronal Modeling. 1st edition. Cambridge: MIT Press; 1989:135-169.
    • (1989) Methods In Neuronal Modeling , pp. 135-169
    • Rinzel, J.1    Ermentrout, G.B.2
  • 25
    • 0015011137 scopus 로고
    • Prediction of repetitive firing behaviour from voltage clamp data on an isolated neurone soma
    • Connor JA, Stevens CF: Prediction of repetitive firing behaviour from voltage clamp data on an isolated neurone soma. J Physiol 1971, 213:31-53.
    • (1971) J Physiol , vol.213 , pp. 31-53
    • Connor, J.A.1    Stevens, C.F.2
  • 26
    • 0026480125 scopus 로고
    • Reduction of conductance-based neuron models
    • Kepler TB, Abbott LF, Marder E: Reduction of conductance-based neuron models. Biol Cybern 1992, 66:381-387.
    • (1992) Biol Cybern , vol.66 , pp. 381-387
    • Kepler, T.B.1    Abbott, L.F.2    Marder, E.3
  • 27
    • 43049129652 scopus 로고    scopus 로고
    • Shear-induced chaos
    • Lin KK, Young LS: Shear-induced chaos. Nonlinearity 2008, 21(5):899-922.
    • (2008) Nonlinearity , vol.21 , Issue.5 , pp. 899-922
    • Lin, K.K.1    Young, L.S.2
  • 28
    • 0035531747 scopus 로고    scopus 로고
    • Strange attractors with one direction of instability
    • Wang Q, Young LS: Strange attractors with one direction of instability. CommunMath Phys 2001, 218:1-97.
    • (2001) CommunMath Phys , vol.218 , pp. 1-97
    • Wang, Q.1    Young, L.S.2
  • 29
    • 0036117030 scopus 로고    scopus 로고
    • From invariant curves to strange attractors
    • Wang Q, Young LS: From invariant curves to strange attractors. Commun Math Phys 2002, 225:275-304.
    • (2002) Commun Math Phys , vol.225 , pp. 275-304
    • Wang, Q.1    Young, L.S.2
  • 30
    • 0141792292 scopus 로고    scopus 로고
    • Strange attractors in periodically-kicked limit cycles and Hopf bifurcations
    • Wang Q: Strange attractors in periodically-kicked limit cycles and Hopf bifurcations. Commun Math Phys 2003, 240:509-529.
    • (2003) Commun Math Phys , vol.240 , pp. 509-529
    • Wang, Q.1
  • 31
    • 50949131740 scopus 로고    scopus 로고
    • On spiking models for synaptic activity and impulsive differential equations
    • Catllá AJ, Schaeffer DG, Witelski TP, Monson EE, Lin AL: On spiking models for synaptic activity and impulsive differential equations. SIAM Rev 2008, 50:553-569.
    • (2008) SIAM Rev , vol.50 , pp. 553-569
    • Catllá, A.J.1    Schaeffer, D.G.2    Witelski, T.P.3    Monson, E.E.4    Lin, A.L.5
  • 32
    • 0001274780 scopus 로고    scopus 로고
    • Computing Lyapunov spectra with continuous Gram-Schmidt orthonormalization
    • Christiansen F, Rugh F: Computing Lyapunov spectra with continuous Gram-Schmidt orthonormalization. Nonlinearity 1997, 10:1063-1072.
    • (1997) Nonlinearity , vol.10 , pp. 1063-1072
    • Christiansen, F.1    Rugh, F.2
  • 33
    • 84950039810 scopus 로고
    • Weak coupling of strongly nonlinear, weakly dissipative identical oscillators
    • Ashwin P: Weak coupling of strongly nonlinear, weakly dissipative identical oscillators. Dyn Syst 1989, 10(3):2471-2474.
    • (1989) Dyn Syst , vol.10 , Issue.3 , pp. 2471-2474
    • Ashwin, P.1
  • 34
    • 0034271535 scopus 로고    scopus 로고
    • Isochronicity-induced bifurcations in systems of weakly dissipative coupled oscillators
    • Ashwin P, Dangelmayr G: Isochronicity-induced bifurcations in systems of weakly dissipative coupled oscillators. Dyn Stab Syst 2000, 15(3):263-286.
    • (2000) Dyn Stab Syst , vol.15 , Issue.3 , pp. 263-286
    • Ashwin, P.1    Dangelmayr, G.2
  • 35
    • 27544493127 scopus 로고    scopus 로고
    • Reduced dynamics and symmetric solutions for globally coupled weakly dissipative oscillators
    • Ashwin P, Dangelmayr G: Reduced dynamics and symmetric solutions for globally coupled weakly dissipative oscillators. Dyn Syst 2005, 20(3):333-367.
    • (2005) Dyn Syst , vol.20 , Issue.3 , pp. 333-367
    • Ashwin, P.1    Dangelmayr, G.2
  • 36
    • 4244104642 scopus 로고
    • Dephasing and bursting in coupled neural oscillators
    • Han SK, Kurrer C, Kuramoto Y: Dephasing and bursting in coupled neural oscillators. Phys Rev Lett 1995, 75:3190-3193.
    • (1995) Phys Rev Lett , vol.75 , pp. 3190-3193
    • Han, S.K.1    Kurrer, C.2    Kuramoto, Y.3
  • 37
    • 55849138986 scopus 로고    scopus 로고
    • Neuronal networks with gap junctions: A study of piecewise linear planar neuron models
    • Coombes S: Neuronal networks with gap junctions: a study of piecewise linear planar neuron models. SIAM J Appl Dyn Syst 2008, 7(3):1101-1129.
    • (2008) SIAM J Appl Dyn Syst , vol.7 , Issue.3 , pp. 1101-1129
    • Coombes, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.