Boston University / Mathematics Department / People / Faculty
Dr. Kopell's
homepage at the Center for BioDynamics
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C. Borgers and N. Kopell, Gamma
oscillations and stimulus selection, Neural Computation, In Press (2007)
N. Kopell, D. Pervouchine, H.G. Rotstein, T. Netoff and M. Whittington. Multiple rhythms and switches in the nervous system, Proceedings of The Second International Symposium on the Frontiers of Applied Mathematics, Conference in honor of the 90th birthday of C.C. Lin, Beijing 2006. Din-Yu Hsieh, Meirong Zhang & Weitao Sun . eds., World Scientific Publishing Co 2007. pp 1-18.
C.D. Behn, E.Brown, T. Scammell and N. Kopell, Mathematical model of network
dynamics governing sleep-wake patterns in mice. J.
Neurophysiol 2007 Jun; 97(6):3828-40. Epub 2007 Apr 4.
J. Beshel, N. Kopell and L. Kay, Olfactory
bulb gamma oscillations are enhanced with task demands, J.
Neurosci., 2007 Aug 1;27(31):8358-65.
A. Tort, H. Rotstein, T. Dugladze, T. Gloveli and N. Kopell, On the formation of gamma-coherent cell
assemblies by oriens lacunosum-moleculare interneurons in the
hippocampus, Proc. Nat. Acad. Science. U S A. 2007 Aug
14;104(33):13490-5. Epub 2007 Aug 6.
R. Silver, K. Boahen, S. Grillner, N. Kopell, K. L. Olsen, Neurotech for neuroscience: Unifying
concepts, organizing principles, and emerging tools. J. Neurosci.,
27(44): 11807-11819, 2007.
T. Dugladze, I. Vida., A.B. Tort., A.Gross., J.Otahal, U. Heinemann,
N.Kopell. and T. Gloveli. Impaired
hippocampal rhythmogenesis in a mouse model of mesial temporal lobe
epilepsy, IN Press Proc. Nat. Acad. Sci. 104 (44): 17530, 2007.
M.O. Cunningham, D. Pervouchine, C. Racca, N. Kopell, C.H. Davies,
R.S. G. Jones, R.D. Traub and M.A. Whittington, Neuronal metabolism
governs cortical network response rate. Proc. Nat. Acad. Sci., 103:
5597-601 (2006)
D. Pervouchine, T. Netoff, H. Rotstein, J. White and N. Kopell, "Low dimensional maps ecoding dynamics in the entorhinal cortex and hippocampus" Neural Computation, 18: 2617-50, (2006)
G. Soto, N. Kopell, and K. Sen "Network architecture, receptive fields and neuromodulation: A computational study of the functional implications of cholinergic modulation in primary auditory cortex." J. Neurophysiol. 96:2972-83 (2006).
Kuznetsov A., Wilson C. and Kopell N., "Transient high-frequency firing in a coupled-oscillator model of the mesencephalic dopaminergic neuron.", J Neurophysiol. 2006 Feb;95(2):932-47
Rotstein H., Oppermann T., White J. and Kopell N., "The dynamic structure underlying subthreshold oscillations and the onset of spikes in medial entorhinal cortex stellate cells", J. Compt. Neurosci. 21:271-292 (2006)
Sivan E. and Kopell N., " Oscillations and slow patterning in the antennal lobe.", J Comput Neurosci. 2006 Feb; 20 (1):85-96.
S.R Jones and N. Kopell "Local
network parameters can affect inter-network phase lags in central
pattern generators", J Math Biol.
2006 Jan; 52(1):115-40.
Theoden I. Netoff, Matthew I. Banks, Alan D. Dorval, Corey D. Acker, Julie S. Haas, Nancy Kopell, and John A. White "Synchronization in Hybrid Neuronal Networks of the Hippocampal Formation", J Neurophysiol. 93(3):1197-208 (2005)
Clewley R., Rotstein H.G., Kopell N., "A computational tool for the reduction of nonlinear ODE systems possessing multiple scales", Multiscale Modeling and Simulation 4:732-759 (2005)
Gloveli T., Dugladze T., Rotstein H., Traub R., Heinemann U., Monyer H., Whittington M. and Kopell N., "Orthogonal arrangement of rhythm generating microcircuits in the hippocampus", PNAS 102:13295-300 (2005)
C. Borgers and N. Kopell "Effects of noisy drive on rhythms in networks of excitatory and inhibitory neurons", Neural Computation 17(3):557-608 (2005)
Nancy Kopell "Biased Random Walk: A Brief Mathematical Biography", in Complexities: Women in Mathematics 1:349-354 (2005)
Steve Kunec and Michael E. Hasselmo and Nancy Kopell "Encoding and Retrieval in the CA3 Region of the Hippocampus: A Model of Theta-Phase Separation ", J Neurophysiol 94:70-82 (2005)
Horacio G. Rotstein, Dmitri D. Pervouchine, Corey D. Acker, Martin J. Gillies, John A. White, Eberhardt H. Buhl, Miles A. Whittington, and Nancy Kopell "Slow and fast inhibition and an h-current interact to create a theta rhythm in a model of CA1 interneuron network ", J Neurophysiol 94:1509-1518 (2005)
O. Jensen and P. Goel and N. Kopell and M. Pohja and R. Hari and B. Ermentrout " On the human sensorimotor-cortex beta rhythm: Sources and modeling ", Neuroimage 26(2):347-55 (2005)
Christoph Börgers and Steven Epstein and Nancy J. Kopell "Background gamma rhythmicity and attention in cortical local circuits: A computational study ", PNAS 102(19):7002-7007 (2005)
N. Kopell "Does it Have to be This Complicated? Focus on Single-Column Thalamocortical Network Model Exhibiting Gamma Oscillations, Spindles, and Epileptogenic Bursts", J Neurophysiol 93:1829-1830 (2005)
Kuznetsov A., Kaern M. and Kopell N., "Synchrony in a population of hysteresis-based genetic oscillators", SIAM J. Appl Math 65:392-42 (2004)
Sivan E. and Kopell N., "Mechanism and circuitry for clustering and fine discrimination of odors in insects", Proc Natl Acad Sci 101:17861-6 (2004)
Nancy Kopell and Bard Ermentrout "Chemical and electrical synapses perform complementary
roles in the synchronization of interneuronal networks ", PNAS
101:15482-15487 101:15482-15487 (2004)
Nancy Kopell "A Tree of Fireflies, a Flock of boson Clouds: the review of "Sync. The Emerging Science of Spontaneous Order" by St. Strogatz", Science 300:1878-1879 (2003)
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. 23(30):9761-9769 (2003)
Corey D. Acker, Nancy Kopell, John A. White "Synchronization of Strongly Coupled Excitatory Neurons: Relating Network Behavior to Biophysics", J. Comp. Neurosci. 15(1):71-90 (2003)
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)
Mette S. Olufsen, Miles A. Whittington, Marcelo Camperi, Nancy Kopell "New Roles for the Gamma Rhythm: Population Tuning and Preprocessing", J. Comput. Neurosci 14:35-54 (2003)
Christoph Borgers, Nancy Kopell "Synchronization in networks of excitatory and inhibitory neurons with sparse, random connectivity", Neural Computation 15:509-538 (2003)
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 15(1):53-69 (2003)
D. Pinto, S. Jones, T. Kaper and N. Kopell "Analysis of state-dependent transitions in frequency and long-distance coordination in a model oscillatory cortical circuit", J. Comp. Neurosci. 15(2):283-298 (2003)
David McMillen, Nancy Kopell "Noise-Stabilized Long-Distance Synchronization in Populations of Model Neurons", J. Comp. Neurosci. 15(2):143-157 (2003)
N.S. Sung, J. Gordon, G. Rose, E. Getzoff, S. Kron, J. Onuchic, N. Scherer, DW Sumners and N. Kopell "Educating a new breed of scientists", Science 301:1485 (2003)
Nancy Kopell, Committee on Undergraduate Biology Education to Prepare Research Scientists for the 21st Century "BIO 2010: Transforming Undergraduate Education for Future Research Scientists", National Research Council, the National Academies Press, Washington DC (2003), preprint
Leonid L. Rubchinsky, Nancy Kopell, Karen A. Sigvardt "Modeling facilitation and inhibition of competing motor programs in basal ganglia subthalamic nucleus�pallidal circuits", Proc. of Nat Acad. Sci. USA 100(24):14427-14432 (2003)
H.G. Rotstein, N. Kopell, A.M. Zhabotinsky, I.R. Epstein, "Canard phenomenon and localization of oscillations in the Belousov-Zhabotinsky reaction with global feedback", J. Chem. Phys. 119(17):8824-8832 (2003)
H.G. Rotstein, N. Kopell, A.M. Zhabotinsky, I.R. Epstein, "A canard mechanism for localization in systems of globally coupled oscillators", SIAM J. Appl. Math. 63:1998-2019 (2003)
McMillen D., Kopell N., Hasty J., Collins J.J. "Synchronizing genetic relaxation oscillators with intercell signaling", Proceedings of the National Academy of Sciences USA 99:679-684 (2002)
O. Jensen, M. Pohja, P. Goel, G.B. Ermentrout, N. Kopell, R. Hari "On the physiological basis of the 15-30 Hz motor-cortex rhythm", Proc. of 13th Int. Conf. On Biomagnetism (2002), preprint
N. Kopell and G.B. Ermentrout "Mechanisms of phase-locking and frequency control in pairs
of coupled neural oscillators",
Handbook on Dynamical Systems: Toward applications. Ed. B. Fiedler,
Elsevier
2:3-54 (2002)
R.D. Traub, N. Kopell, A. Bibbig, E.H. Buhl, F.E.N. LeBeau, M.A. Whittington "Gap junctions between interneuron dendrites can enhance synchrony of gamma oscillations in distributed networks", J. Neurosci. 21:9478-9486 (2001)
E. C. Fuchs, H. Doheny, H. Faulkner, A. Caputi, R.D. Traub, A. Bibbig, N. Kopell, M. Whittington, 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)
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)
C. Chow, N. Kopell "Dynamics of spiking neurons with electrical coupling", Neural Computation 12(7):1643-1678 (2000)
M.A. Whittington, R.D. Traub, N. Kopell, G.B. Ermentrout, E.H. Buhl "Inhibition-based rhythms: Experimental and mathematical observation on network dynamics", Int. J. of Psychophysiology 38:315-336 (2000)
N. Kopell, G.B. Ermentrout, M. Whittington, R.D. Traub "Gamma rhythms and beta rhythms have different synchronization properties", Proc. Nat. Acad. Sci. USA 97:1867-1872 (2000)
J. White, M. Banks, R. Pearce, N. Kopell "Networks of interneurons with fast and slow GABA_A kinetics provide substrate for mixed gamma-theta rhythm", Proc. Nat. Acad. Sci. USA 97:8128-8133 (2000)
J. Karbowski, N. Kopell "Multispikes and synchronization in a large-scale neural network with delays", Neural Computation 12:1573-1606 (2000)
S.R. Jones, D. Pinto, T. Kaper, N. Kopell "Alpha-frequency rhythms desynchronize over long cortical distances: a modelling study", J. Comput. Neurosci. 9:271-291 (2000)
G. Medvedev, T. Kaper and N. Kopell "A reaction-diffusion system with periodic front dynamics", SIAM J. Appl. Math 60:1601-1638 (2000)
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 140:69-94 (2000)
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 96:8206-8211 (1999)
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)
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)
C. Chow, J. White, J. Ritt, N. Kopell "Frequency control in synchronous networks of inhibitory neurons", J. Comput. Neurosci. 5:407-420 (1998)
J. White, C. Chow, J. Ritt, C. Soto-Trevino, N. Kopell "Synchronization and Oscillatory Dynamics in Heterogeneous, Mutually Inhibited Neurons ", J. Comp. Neuro. 5:5-16 (1998)
G.B. Ermentrout, N. Kopell "Fine structure of neural spiking and synchronization in the presence of conduction delays", Proc. Nat. Acad. Sci. USA 95:1259-1264 (1998)
N. Kopell, ``Networks of neurons as dynamical systems: from geometry to biophysics'', Quarterly of Appl. Math. 56 (1998) 707-718.
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).
D. Terman, N. Kopell and A. Bose, ``Dynamics of two mutually inhibitory neurons'' Physica D 117:241-275 (1998). [Abstract HTML] [Preprint PDF]
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, N. Kopell "Functional reorganization in thalamocortical networks: Transition between spindling and delta sleep rhythms", Proc. Nat. Acad. Sci. USA 93:15417-15422 (1996)
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.
N. Kopell, Commuting diffeomorphisms, in Global Analysis, Symposia
in Pure Mathematics, American Mathematical Society, Providence 14
(1970) 165-184.
N. Kopell and L.N. Howard, Horizontal bands in the Belousov reaction,
Science, 180 (1973) 1171-1173.
N. Kopell and L.N. Howard, Plane wave solutions to reaction diffusion
equations, Studies in Applied Mathematics, 52 (1973) 291-328.
N. Kopell, Dissipative and non-dissipative structures, Annals of the
New York Academy of Science, 231 (1974) 106-107.
N. Kopell and L.N. Howard, Bifurcation under non-generic conditions,
Advances in Mathematics, 13 (1974) 274-283.
N. Kopell and L.N. Howard, Pattern Formation in the Belousov reaction,
Lectures on Mathematics in the Life Sciences, 7 (1974) 201-216.
L.N. Howard and N. Kopell, Wave trains, shock structures and transition
layers in reaction-diffusion equations, in Mathematical Aspects of
Chemical and Biochemical Problems and Quantum Chemistry, AMS-SIAM
Proceedings 8, American Mathematical Society, Providence, (1974)
274-283.
N. Kopell and L.N. Howard, Bifurcations and trajectories joining
critical points, Advances in Mathematics, 18 (1975) 306-358.
N. Kopell and G. Stolzenberg, Commentary on Bishop's Talk, Historia
Mathematica 2 (1975) 519-521.
L.N. Howard and N. Kopell, Translation, with editorial comments, of E.
Hopf's Abzeigung einer periodischen Losung von einer stationaren
Losungeines Differentialsystems in The Hopf Bifurcation and its
Applications, Applied Mathematical Sciences 19, J. Marsden and M.
McCracken, eds., Springer-Verlag, New York (1978) 163-205.
L.N. Howard and N. Kopell, Slowly varying waves and shocks in
reaction-diffusion equations, Studies in Applied Math., 56 (1977)
95-145.
N. Kopell, Waves, shocks and target patterns in an oscillating chemical
reagent, in Nonlinear Diffusion, Research Notes in Mathematics 14
(1977) 129-154, Pitman.
N. Kopell, Pattern formation in chemistry and biology: a mini-survey of
mechanisms, in Psychology and Biology of Language and Thought: Essays
in Honor of Eric Lenneberg , G. Miller, ed., Academic Press , New
York (1978) 65-85.
N. Kopell, Reaction-diffusion equations and pattern formation, in
Studies in Mathematical Biology , S. Levin, ed. MAA Studies in
Mathematics, Mathematical Association of America 15 (1978)
191-205.
N. Kopell, A geometric approach to boundary layer problems exhibiting
resonance, SIAM J. Applied Math, 37 (1979) 436-458.
N. Kopell, Time periodic but spatially irregular solutions to a model
reaction-diffusion equation, in Nonlinear Dynamics, R. Helleman, ed.,
N.Y. Academy of Sciences, New York (1980) 397-409.
N. Kopell, The singularly perturbed turning point problem: a geometric
approach, in Singular Perturbations and Asymptotics. R.
Meyer ed., Academic Press, New York (1980) 173-190.
N. Kopell and L.N. Howard, Target patterns and horseshoes from a
perturbed central force problem: some temporally periodic solutions to
reaction-diffusion equations, Studies in Appl. Math., 64 (1981) 1-56.
N. Kopell and S. Parter, A complete analysis of a model nonlinear
equation having a continuous locus of turning points, Advances in Appl.
Math., 2 (1981) 212-238.
N. Kopell and L.N. Howard, Target patterns and spiral solutions to
reaction-diffusion equations with more than one space dimension,
Advances in Appl. Math. 2 (1981), 417-449.
N. Kopell, Target pattern solutions to reaction-diffusion equations in
the presence of impurities, Advances in Appl. Math. 2 (1981) 389-399.
N. Kopell and R. Washburn, Chaotic motions in the two-degree of freedom
swing equations, IEEE Transactions on Circuits and Systems, Special
Issue on Power Systems, Vol. CAS-29, 11 (1982) 738-746.
N. Kopell, Frequency plateaus in a chain of weakly coupled oscillators,
in Nonlinear Partial Differential Equations, Contemporary Mathematics,
17, J. Smoller, ed. American Mathematical Society, Providence (1982)
401-404.
N. Kopell and G.B. Ermentrout, Coupled Oscillators and Mammalian Small
Intestines, in Oscillation in Mathematical Biology, Lecture Notes in
Biomathematics, 51, J.P.E. Hodgson, ed., Springer-Verlag, New York
(1982) 24-36
G.B. Ermentrout and N. Kopell, Frequency plateaus in a chain of weakly
coupled oscillators, I, SIAM J. on Math. Anal. 15 (1984), 215-237.
N. Kopell, Forced and coupled oscillators in biological applications,
Proc. of the 1983 International Congress, Warsaw, North Holland,
Amsterdam (1984) 1645-1660.
N. Kopell, Symmetry and coherence in a chain of coupled oscillators, in
Chaos in Nonlinear Dynamical Systems, J. Chandra, ed., SIAM,
Philadelphia (1984) 86-93.
N. Kopell, Invariant manifolds and the initialization problem for some
atmospheric equations, Physica D 14 (1985) 203-215.
G.B. Ermentrout and N. Kopell, Parabolic bursting in an excitable
system coupled with a slow oscillation, SIAM J. Appl. Math. 46
(1986) 233-253.
N. Kopell and G.B. Ermentrout, Subcellular oscillations and bursting,
Math. Biosciences, 78 (1986) 265-291.
N. Kopell and D. Ruelle, Bounds on complexity in reaction-diffusion
systems, SIAM J. Appl. Math., 46 (1986) 68-80,
N. Kopell, Phase methods for coupled oscillators and related topics: an
annotated bibliography, J. Statistical Physics 44 (1986) 1035-1042.
N. Kopell, Coupled oscillators and locomotion by fish, in Nonlinear
Oscillations in Biology and Chemistry, H. Othmer, ed. Lecture Notes in
Biomathematics 66, Springer-Verlag, New York (1986) 166-174.
N. Kopell, Modelling C.P.G.'s: a robust approach, in Neurobiology of
Vertebrate Locomotion, S. Grillner, P.S.G. Stein, D.G. Stuart, H.
Forssberg and R. Herman, Eds.,Wenner-Grenn Center International
Symposium Series, 45 Macmillan, London, (1986)383-385.
N. Kopell and G.B. Ermentrout, Symmetry and phaselocking in chains of
weakly coupled oscillators, Communications on Pure and Applied
Mathematics, 39 (1986) 623-660.
N. Kopell, Toward a theory of modelling central pattern generators, in
Neural Control of Rhythmic Movements, A. Cohen, S. Grillner, S.
Rossignol, eds., J. Wiley , New York (1987) 369-413.
N. Kopell and G.B. Ermentrout, Coupled oscillators and the design of
central pattern generators, Math. Biosciences, 90 (1988) 87-109.
N. Kopell, Chains of oscillators and the effects of multiple coupling,
Appendix to Studies of the lamprey Central Pattern Generator for
Locomotion: a close relationship between modeling and experimentation,
by A.H. Cohen, in Dynamic Patterns in Complex Systems, S. Kelso, ed.,
World Scientific Publishers, (1988) 156-161.
G.B. Ermentrout and N. Kopell, Some mathematical questions concerning
central pattern generators, in Theoretical Models of Cell Signalling,
A. Goldbeter, ed., Academic Press, New York (1989) 89-98.
Boston University / Mathematics Department / People / Faculty