Boston University / Mathematics Department / People / Faculty
Dr. Kopell's homepage at
the Center for BioDynamics
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MA Kramer, AK Roopun, LM Carracedo, M Kaiser, CH Davies, RD Traub , MA Whittington and N. Kopell, A mechanism for rhythm generation through period concatenation, PLoS Comput Biol. 2008 Sep 5;4(9):e1000169.
MA. Kramer . RD Traub and N. Kopell, New dynamics in cerebellar Purkinje cells: limit cycle canards. Phys Rev Lett. 2008 Aug 8;101(6):068103. Epub 2008 Aug 8.
H. Rotstein, M. Wechselberger and N.Kopell, Canard-induced mixed-mode oscillations in a medial entorhinal cortex layer II stellate cell model, SIAM J. Appl. Dyn. Syst. Volume 7, Issue 4, pp. 1582-1611 (2008).
McCarthy, E.N. Brown and N. Kopell, Potential network mechanisms mediating propofol-induced paradoxical excitation, J Neurosci. 2008 Dec 10;28(50):13488-504..
A. Tort, MA Kramer, C. Thorn, D. Gibson, Y. Kubota, AN Graybiel and N. Kopell, Dynamic cross-couplings of local field potential oscillations in rat striatum and hippocampus during performance of T-maze task, Proc Natl Acad Sci U S A. 2008 Dec 23;105(51):20517-22. Epub 2008 Dec 12.
S. Middleton. J. Jalics, T. Kispersky, FEN LeBeau, N. Kopell. MA Whittington and MO Cunningham, NMDA Receptor-dependent modulation of different rhythm-generating microcircuits in entorhinal cortex, Proc. Natl. Acad. Sci. U S A. 2008 Nov 25; 105(47):18572-7. Epub 2008 Nov 7.
C. Borgers. S. Epstein and N. Kopell, Gamma oscillations mediate stimulus competition and attentional selection in a cortical network model. Proc Natl Acad Sci U S A. 2008 Nov 18;105(46):18023-8. Epub 2008 Nov 12.
AK. Roopun MA Kramer, L.Carracedo, M.Kaiser, C. Davies, RD Traub, N.. Kopell, MA Whittington, Temporal interactions between cortical rhythms, Frontiers in Neuroscience, 2008 Dec;2(2):145-54. Epub 2008 Dec 15.
L. Kay, J. Beshel, J. Brea, C. Martin. D. Rojas-Liban and N. Kopell, Olfactory oscillations: the what, how and what for. Trends in the Neurosci. 2009 iTrends Neurosci. 2009 Apr;32(4):207-14. Epub 2009 Feb 23.
M Shamir, O. Ghitza, S. Epstein, N. Kopell, Representations of time-varying stimuli by a network exhibiting oscillations on a faster time scale. PLoS Comput. Biol. 2009 May;5(5):e1000370. Epub 2009 May 1.
D. Vierling-Claasen and N. Kopell, The dynamics of a periodically forced cortical microcircuit, with an application to schizophrenia, SIAM J. Applied Dynamical systems, URL: http://link.aip.org/link/?SJA/8/710, DOI: 10.1137/080738052 June 2009.
P. Wulff, A.A Ponomarenko, M. Bartos, T. M. Korotkova, E.C. Fuchs, F. Bähner, M. Both, A.B. L. Tort, N. Kopell, W. Wisden, and H. Monyer, Hippocampal theta rhythm and its coupling with gamma oscillations require fast inhibition onto parvalbumin-positive interneurons, Proc Natl Acad Sci U S A. 2009 Mar 3;106(9):3561-6. Epub 2009 Feb 9.
N. Kopell, C. Borgers, D. Pervouchine, P. Malerba, and A. B.L.Tort. Gamma and theta rhythms in biophysical models of hippocampal circuits. To appear in Hippocampal Microcircuits: A Computational Modeller's Resource Book. Springer 2009
T. Gloveli, N. Kopell and T. Dugladze. Neuronal Activity Patterns during Hippocampal Network Oscillations in Vitro. To appear in Hippocampal Microcircuits: A Computational Modeller's Resource Book. Springer 2009
Nancy Kopell ``A Tree of Fireflies, a Flock of Boston Clouds'' Science 300:1878-1879, 2003. [PDF]
Mark O. Cunningham, Ceri H. Davies, Eberhard H. Buhl, Nancy Kopell and Miles A. Whittington ``Gamma oscillations induced by kainate receptor activation in the entorhinal cortex in vitro'' J. Neurosci., submitted 2003. [PDF]
Horacio G. Rotstein, Nancy Kopell, Anatol M. Zhabotinsky and Irving R. Epstein ``A canard mechanism for localization in systems of globally coupled oscillators'' SIAM J. Applied Math. 2003, accepted. [Postscript]
Corey D. Acker, Nancy Kopell, John A. White ``Synchronization of Strongly Coupled Excitatory Neurons: Relating Network Behavior to Biophysics'' J. Comp. Neurosci. 2003, in press. [PDF]
David J. Pinto, Stephanie R. Jones, Tasso J. Kaper, Nancy Kopell ``Analysis of state-dependent transitions in frequency and long-distance coordination in a model oscillatory cortical circuit'' J. Comp. Neurosci. 2003[PDF]
Stephanie R. Jones, Brian Mulloney, Tasso J. Kaper, and Nancy Kopell ``Coordination of Cellular Pattern-Generating Circuits that Control Limb Movements: The Sources of Stable Differences in Intersegmental Phases'' J. Neurosci. 23:3457-3468 (2003) [PDF]
Mette S. Olufsen, Miles A. Whittington, Marcelo Camperi, Nancy Kopell ``New Roles for the Gamma Rhythm: Population Tuning and Preprocessing for the Beta Rhythm'' J. Comput. Neurosci. 2003, in press. [PDF]
Christoph Borgers, Nancy Kopell ``Synchronization in networks of excitatory and inhibitory neurons with sparse, random connectivity'' Neural Computation 15:509-538 (2003). [PDF]
G.S. Medvedev, C.J. Wilson, J.C. Callaway, Nancy Kopell ``Dendritic synchrony and transient dynamics in a coupled oscillator model of dopaminergic neuron'' J. Comput. Neurosci, in press (2003). [PostScript]
O. Jensen, M. Pohja, P. Goel, B. Ermentrout, N. Kopell, and R. Hari. ``On the Physiological Basis of the 15-30 Hz Motor-Cortex Rhythm'', submitted.
D. McMillen, N. Kopell, J. Hasty and J.J. Collins. ``Synchronizing genetic relaxation oscillators with intercell signaling'', Proc. Nat. Acad. Sci (2002) [Preprint PDF]
N. Kopell and G.B. Ermentrout. ``Mechanisms of phase-locking and frequency control in pairs of coupled neural oscillators'', for Handbook on Dynamical Systems, vol. 2: Toward applications. Ed. B. Fiedler, Elsevier, pp 3-5. (2002)
E. C. Fuchs, H. Doheny, H. Faulkner, A. Caputi, R.D. Traub, A. Bibbig, N. Kopell, M. Whittington, and H. Monyer. ``Genetically altered AMPA-type glutamate receptor kinetics in interneurons disrupt long-range synchrony of gamma neurons'', Proc. Nat. Acad. Sci USA 98 3571-3576 (2001).
R.D. Traub, N. Kopell, A. Bibbig, E.H. Buhl, F.E.N. LeBeau, and M.A. Whittington. ``Gap junctions between interneuron dendrites can enhance synchrony of gamma oscillations in distributed networks''. J. Neurosci. 21(23): 9478-9486 (2001).
G. S. Medvedev and N. Kopell, ``Synchronization and transient dynamics in chains of electrically coupled FitzHugh-Nagumo oscilllations.'' SIAM J. Appl. Math 61(5): 1763-1801 (2001). [PS 13 MB]
S. R. Jones, D. Pinto, T. Kaper and N. Kopell, ``Alpha-frequency rhythms desynchronize over long cortical distances: a modeling study'', J. Comput. Neurosci., 9(3): 271-291 (2000). [Preprint PDF]
J. White, , M. Banks, R. Pearce and N. Kopell ``Networks of interneurons with fast and slow GABAA kinetics provide substrate for mixed gamma-theta rhythm'', Proc. Nat. Acad. Sci. USA, 97: 8128-8133 (2000). [Reprint PDF from PNAS]
M.A. Whittington, R.D. Traub, N. Kopell, G.B. Ermentrout and E.H. Buhl, ``Inhibition-based rhythms: Experimental and mathematical observation on network dynamics'', Int. J. of Psychophysiol., in press. [Preprint HTML]
N. Kopell and G.B. Ermentrout ``Mechanisms of phase-locking in pairs of coupled neural oscillators'', to appear in Handbook on Dynamical Systems: Toward applications. Eds B. Fiedler, G. Iooss, N. Kopell, Elsevier, 2000. [PS, no figs] [Figures, GZIP TAR] [Figures, ZIP file]
C. Chow and N. Kopell, ``Dynamics of spiking neurons with electrical coupling'', Neural Comp., 12: 1643-1678 (2000). [GZIP PS from C. Chow]
J. Karbowski and N. Kopell ``Multispikes and synchronization in a large neural network with temporal delays'', Neural Comp., 12: 1573-1606 (2000). [PDF]
G. Medvedev, T. Kaper and N. Kopell, ``A reaction-diffusion system with periodic front dynamics'' , SIAM J. Appl. Math., 60: 1601-1638 (2000). [Reprint from SIAP (may require subscription)]
N. Kopell, ``We got rhythm: Dynamical systems of the nervous system'', published version of the 1998 Gibbs Lecture of the AMS, Notices of the AMS, 47: 6-16 (2000).
A. Bose, N. Kopell, D. Terman,, ``Almost synchronous solutions for pairs of neurons coupled by excitation'', Physica D 140 (2000) 69-94. [Preprint PDF]
N. Kopell, G. B. Ermentrout, M. A. Whittington and R. D. Traub. ``Gamma rhythms and beta rhythms have different synchronization properties'' PNAS 97:1867-1872 (2000). [Abstract HTML] [Preprint PS] [Reprint from PNAS (requires sign in).]
F. Nadim, Y. Manor, N. Kopell and E. Marder, ``Synaptic depression creates a switch that controls the frequency of an oscillator circuit''. Proc. of Nat Acad. Sci. USA 96 (1999) 8206-8211. [Preprint PDF from F. Nadim]
T. LoFaro and N. Kopell, ``Timing regulation in a network reduced from voltage-gated equations to a one-dimensional map'', J. Math Biol. 38: 479-533. (1999) [Abstract HTML] [Preprint PDF]
Y. Manor, F. Nadim, J. Ritt, S. Epstein, E. Marder, N. Kopell ``Network oscillations generated by balancing asymmetric inhibition in passive neurons'', J. Neurosci., 19: 1765-2779 (1999). [Abstract HTML] [Preprint PDF]
N. Kopell, ``Networks of neurons as dynamical systems: from geometry to biophysics'', Quarterly of Appl. Math. 56 (1998) 707-718.
C. Chow, J. White, J. Ritt and N. Kopell, ``Frequency control in synchronous networks of inhibitory neurons'', J. Comput. Neurosci., 5: 407-420 (1998). [Abstract HTML] [Preprint PDF] [Preprint GZIP PS from C. Chow]
N. Kopell, L. Abbott and C. Soto-Trevino, ``On the behavior of a neural oscillator electrically coupled to a bistable element'', Physica D, 121: 367-395 (1998). [Abstract HTML] [Preprint PDF]
D. Terman, N. Kopell and A. Bose, ``Dynamics of two mutually inhibitory neurons'' Physica D 117:241-275 (1998). [Abstract HTML] [Preprint PDF]
G.B. Ermentrout and N. Kopell ``Fine structure of neural spiking and synchronization in the presence of conduction delays'' Proc. Nat. Acad. Sci., USA 95:1259-1264 (1998). [Abstract HTML] [Preprint -figs PDF] [Figure 1 PDF] [Figures 2 and 3 PDF]
J. White, C. Chow, J. Ritt, C. Soto-Trevino and N. Kopell, ``Synchronization and oscillatory dynamics in heterogeneous, mutually inhibited neurons,'' J. Comp. Neurosci., 5: 5-16 (1998). [Abstract HTML] [Preprint PDF] [Preprint GZIP PS from C. Chow]
M. Hayes, T. Kaper, N. Kopell and K. Ono, ``On the application of geometric singular perturbation theory to some classical two-point boundary value problems'', Bifurcation and Chaos, : 189-209 (1998).
F. Skinner, N. Kopell and B. Mulloney, ``How does the crayfish swimmeret system work: Insights from nearest neighbor coupled models'', J. Comp. Neurosci., 4 (1997) 151-160
J.M. Weimann, P. Skiebe, H.-G Heinzel, C. Soto, N. Kopell, J.C. Jorge-Rivera and E. Marder, ``Modulation of network dynamics in the crab stomatogastric ganglion by crustacean cardioactive peptide'', J. Neurosci. 17 (1997) 1748-1760.
D. Terman, A. Bose and N. Kopell, ``Functional reorganization in thalamocortical networks: Transition between spindling and delta sleep rhythms'', Proc. Nat. Acad. Sci. USA 93 (1996), 15417-15422
C. Soto-Trevino, N. Kopell and D. Watson, ``Parabolic bursting revisited'', J. Math. Biol. 35 (1996) 114-128.
C. Jones, T. Kaper, and N. Kopell, ``Tracking invariant manifolds up to exponentially small errors,'' SIAM J. Math., Anal. 27 (1996) 558-577.
D. Somers and N. Kopell, ``Waves and synchrony in arrays of oscillators of relaxation and non-relaxation type'', Physica D 89 (1995) 169-183.
N. Kopell and M. Landman, ``Spatial structure of the focusing singularity of the nonlinear Schrodinger equation: a geometric analysis'', SIAM J. Appl. Math. 55 (1995) 1297-1323.
N. Kopell, ``Chains of Coupled Oscillators'', in Handbook of Brain Theory and Neural Networks, M. Arbib, ed., MIT Press, Cambridge (1995) 178-183.
N. Kopell and D. Somers, ``Anti-phase solutions in relaxation oscillators coupled through excitatory interactions'', J. Math. Biol. 33 (1995) 261-280.
S.K. Tin, N. Kopell and C.K.R.T. Jones, ``Invariant manifolds and singularly perturbed boundary value problems'', SIAM J. Num. Anal. (special volume in honor of S. Parter) 31 (1994) 1558-1576.
N. Kopell and G. LeMasson, ``Rhythmogenesis, amplitude modulation and multiplexing in a cortical architecture'', Proc. Nat. Acad. Sci. (USA) 91 (1994) 10586-10590.
F. Skinner, N. Kopell and E. Marder, ``Mechanisms for oscillation and frequency control in networks of mutually inhibitory relaxation oscillators'', J. Comput. Neurosci., 1 (1994) 69-87.
G.B. Ermentrout and N. Kopell, ``Learning of phase-lags in coupled neural oscillators'', Neural Computation 6 (1994) 225-241.
G.B. Ermentrout and N. Kopell, ``Inhibition-produced patterning in chains of coupled nonlinear oscillators'', SIAM J. Appl. Math. 54 (1994) 478-507.
T. LoFaro, N. Kopell, E. Marder and S. Hooper, ``Subharmonic coordination in networks of neurons with slow conductances'', Neural Computation 6 (1994) 69-84.
C. Jones and N. Kopell, ``Tracking invariant manifolds with differential forms in singularly perturbed equations'', J. Diff. Equa. 108 (1994) 64-88.
D. Somers and N. Kopell, ``Rapid synchronization through fast threshold modulation'', Biol. Cybern. 68 (1993), 393-407.
N. Kopell, ``Dynamical Systems and the Geometry of Singularly Perturbed Equations'', in From Topology to Computation: Proceedings of the Smalefest, Springer-Verlag, New York, (1993).
A.H. Cohen, G.B. Ermentrout, T. Kiemel, N. Kopell, K. Sigvardt and T. Williams, ``Modelling of intersegmental coordination in the lamprey central pattern generator for locomotion'', Trends in the Neurosciences, 15 (1992), 434-438.
C. Jones, N. Kopell and R. Langer, ``Construction of the FitzHugh-Nagumo pulse using differential forms'', in Pattern and Dynamics in Reactive Media, IMA Volumes in Mathematics and its Applications, 37, H. Swinney, G. Aris, and D. Aronson, eds., Springer-Verlag, New York (1991) 101-116.
N. Kopell, G.B. Ermentrout and Thelma Williams, ``On chains of neural oscillators forced at one end'', SIAM J. Appl. Math. 51 (1991), 1397-1417.
G.B. Ermentrout and N. Kopell, ``Multiple pulse interactions and averaging in coupled neural oscillators'', J. Math. Biol., 29 (1991), 195-217.
T. Williams, K. Sigvardt, N. Kopell, G.B. Ermentrout and M. Remler, ``Forcing of coupled nonlinear oscillators: studies of intersegmental coordination in the lamprey locomotor central pattern generator'', J. Neurophysiol., 64 , 1990, 862-871.
N. Kopell, W. Zhang and G.B. Ermentrout, ``Multiple coupling in chains of oscillators'', SIAM J. Math. Anal. 21 (1990), 935-953.
D.G. Aronson, G.B. Ermentrout and N. Kopell, ``Amplitude response of coupled oscillators'', Physica D 41 (1990), 403-449.
N. Kopell and G.B. Ermentrout, ``Phase transitions and other phenomena in chains of oscillators'', SIAM J. Appl. Math, 50 (1990) 1014-1052.
G.B. Ermentrout and N. Kopell, ``Oscillator death in systems of coupled
neural oscillators'', SIAM J. Appl. Math, 50 (1990), 125-146.
Boston University / Mathematics Department / People / Faculty