S. Vijayan, N. Kopell, Thalamic model of awake alpha oscillations and implications for stimulus processing. PNAS, 2012; 109(45):18553-8.

M. Ainsworth, S. Lee, M.O. Cunningham, R.D. Traub, N. Kopell, M.A. Whittington, Rates and Rhythms: A synergistic view of frequency and temporal coding in neuonal networks. Neuron, 2012; 75(4):572-83.

C. Borgers, G. Talei Franzesi, F. LeBeau, E. Boyden, and N. Kopell. Minimal size of cell assemblies coordinated by gamma oscillations. PloS Comp. Biol., 2012; 8(2):e1002362.

S. Ching, P.L. Purdon, S. Vijayan, N. Kopell, and E.N. Brown, A neurophysiological-metabolic model for the burst suppression. PNAS, 2012; 109(8):3095-100.

M. M. McCarthy, S. Ching, M.A. Whittington, and N. Kopell, Dynamical changes in neurological disease and anesthesia. Current Opinion in Neurobiology, 2012; 22(4):693-703.

P. Malerba and N. Kopell, Phase resetting reduces theta-gamma interaction to a one-dimensional map. J. Math Biol., April 2012:1-26.

M.M. McCarthy and N. Kopell, Rebound spiking in a neuronal system with a slow current and fast inhibition. SIAM J. Appl. Dynamics, 2012, resubmitted.

E. Munro and N. Kopell, Subthreshold somatic voltage in neocortical pyramidal cells can control whether spikes propagate from the axonal plexus to axon terminals: a model study. J. Neurophysiol., 2012;107(10):2833-52. PMID: 22378167

N. Kopell, M.A. Whittington and M.A. Kramer, Neuronal assembly dynamics in the beta1 frequency range permits short- term memory. Proc. Natl. Acad. Sci. U. S. A., 2011;108(9):3779-84. PMID: 21321198

M. Ainsworth, S. Lee, M.O. Cunningham, A.K. Roopun, R.D. Traub, N.J. Kopell, and M.A. Whittington, Dual gamma rhythm generators control interlaminar synchrony in auditory cortex. J. Neurosci., 2011;31(47):17040-51. PMID: 22114273

M.M. McCarthy, C. Moore-Kochlacs, X. Gu, E.S. Boyden, X. Han., and N. Kopell, Striatal origin of the pathologic beta oscillations in Parkinson's disease. Proc. Nat. Acad. Sci. U. S. A., 2011;108(28):11620-5. PMID: 21697509

A.B. Tort, R. Komorowski, N. Kopell, and H. Eichenbaum, A mechanism for the formation of hippocampal neuronal firing patterns that represent what happens where. Learn. Mem., 2011;18(11):718-27. PMID: 22021254

M. Desai, I. Kahn, U. Knoblich, J. Bernstein, H. Atahallah, N. Kopell, R.L. Buckner, A.M. Graybiel, C.I. Moore, and E.S. Boyden, Mapping brain networks in awake mice using combined optical neural control and fMRI. J. Neurophysiol., 2011;105(3):1393-405. PMID: 21160013

A.B. Tort, A. Fontanini, M.A. Kramer, L.M. Jones-Lush, N.J. Kopell, and D.B. Katz, Cortical networks produce three distinct 7-12 Hz rhythms during single sensory responses in the awake rat. J. Neurosci., 2010;30(12):4315-24. PMID: 20335467

N. Kopell, M. Kramer, P. Malerba, and M.A. Whittington, Are different rhythms good for different functions? Front. Hum. Neurosci., 2010;4:187. PMID: 21103019

A.B. Tort, R. Komorowski, H. Eichenbaum, and N. Kopell, Measuring phase-amplitude coupling between neuronal oscillations of different frequencies. J. Neurophysiol., 2010;104(2):1195-210. PMID: 20463205

S. Ching, A. Cimenser, P. Purdon, E.N. Brown, and N. Kopell, Thalamocortical model for a propofol-induced alpha-rhythm associated with loss of consciousness. Proc. Natl. Acad. Sci. U. S. A., 2010;107(52):22665-70. PMID: 21149695

N. Kopell, C. Borgers, D. Pervouchine, P. Malerba, and A.B.L. Tort, Gamma and theta rhythms in biophysical models of hippocampal circuits. In Hippocampal microcircuits: A computational modeller's resource book, V. Cutsuridis, B.F. Graham, S. Cobb, and I. Vida, eds., Springer, 2010;423-57. Code for figures: Fig. 1, Fig. 2, Figs. 3 and 4.

T. Gloveli, N. Kopell and T. Dugladze, Neuronal activity patterns during hippocampal network oscillations in nitro. In Hippocampal microcircuits: A computational modeller's resource book, V. Cutsuridis, B.F. Graham, S. Cobb, and I. Vida, eds., Springer, 2010.

L. Kay, J. Beshel, J. Brea, C. Martin, D. Rojas-Libano, and N. Kopell, Olfactory oscillations: The what, how and what for. Trends Neurosci., 2009;32(4):207-14. PMID: 19243843

M. Shamir, O. Ghitza, S. Epstein, and N. Kopell, Representation of time-varying stimuli by a network exhibiting oscillations on a faster time scale. PLoS Comput. Biol., 2009;5(5):e1000370. PMID: 19412531

D. Vierling-Claasen and N. Kopell, The dynamics of a periodically forced cortical microcircuit, with an application to schizophrenia. SIAM J. Appl. Dyn. Syst., 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. Bahner, M. Both, A.B. 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;106(9):3561-6. PMID: 19204281

A. Tort, R. Komorowski, J. Manns, N. Kopell, and H. Eichenbaum, Theta-gamma coupling increases during the learning of item-context associations. Proc. Natl. Acad. Sci. U. S. A., 2009;106(49):20942-7. PMID: 19934062

S. Lee, K. Sen and N. Kopell, Cortical gamma rhythms are modulated by NMDAR-mediated spike timing dependent plasticity in a biophysical model. PLoS Comput. Biol., 2009;5(12):e1000602. PMID: 20011119

N. Kopell, R.D. Traub and M.A. Whittington, Modeling rhythms: From physiology to function. Publication of Society for Neuroscience, 2009, Short Course #2, Rhythms of the Neocortex: Where do they come from and what are they good for? http://www.sfn.org/shortcourses

M.A. Whittington, R.D. Traub and N. Kopell, Diverse origins of network rhythms in cortical local circuits. Publication of Society for Neuroscience 2009, Short Course #2, Rhythms of the Neocortex: Where do they come from and what are they good for? http://www.sfn.org/shortcourses

M.A. Whittington, N. J. Kopell and R.D. Traub, What are the local circuit design features concerned with coordinating rhythms? Ms prepared for Strungman Forum: Dynamic coordination in the brain: From neurons to mind. 2009.

J. Brea, L. Kay and N. Kopell, Biophysical model for gamma rhythms in the olfactory bulb via subthreshold oscillations. Proc. Natl. Acad. Sci. U. S. A., 2009;106(51):21954-9. PMID: 19996171

M. Krupa, N. Popovic, N. Kopell, and H. Rotstein, Mixed-mode oscillations in a three time-scale model of oscillations for the dopaminergic neuron. Chaos, 2008;18:015106. PMID: 18377087

M. Krupa, N. Popovic and N. Kopell, Mixed-mode oscillations in three time-scale systems: A prototypical example. SIADS Online, 2008;7(2):361-420.

D. Vierling-Claassen, P. Seikmeier, S. Stufflebeam, and N. Kopell, Modeling GABA alterations in schizophrenia: A link between impaired inhibition and altered gamma and beta range auditory entrainment. J. Neurophysiol., 2008;99(5):2656-71. PMID: 18287555

C. G. Diniz Behn, N. Kopell, E.N. Brown, T. Mochizuki, and T.E. Scammell, Delayed orexin signaling consolidates wakefulness and sleep: Physiology and modeling. J. Neurophysiol., 2008; 99(6): 3090-103. PMID: 18417630

M. Kramer, A. Tort, and N. J. Kopell, Sharp edge artifacts and spurious coupling in EEG frequency comodulation measures. J. Neurosci. Methods, 2008;170(2):352-7. PMID: 18328571

C. Borgers and N.J. Kopell, Gamma oscillations and stimulus selection. Neural Comput., 2008;20(2):383-414. PMID: 18047409

A. K. Roopun, M.A. Kramer, L. Carracedo, M. Kaiser, C. Davies, R.D. Traub, N. Kopell, and M.A. Whittington, Period concatenation underlies interactions between gamma and beta rhythms in neocortex. Front. Cell. Neurosci., 2008;2:1. PMID: 18946516 doi:10.3389/neuro.03.001.2008 (http://sandbox.frontiersin.org/cellularneuroscience/paper/10.3389/neuro.03/001.2008/)

M.M. McCarthy, E.N. Brown, and N. Kopell, Potential network mechanisms mediating electroencepholagraphic beta rhythm changes during propofol-induced paradoxical excitation. J. Neurosci., 2008;28(50):13488-504. PMID: 19074022

A. Tort, M.A. Kramer, C. Thorn, D. Gibson, Y. Kubota, A.N. Graybiel, and N. Kopell, Dynamic cross-frequency couplings of local field potential oscillations in rat striatum and hippocampus during performance of a T-maze task. Proc. Natl. Acad. Sci. U. S. A., 2008;105(51):20517-22. PMID: 19074268

M.A. Kramer, A.K. Roopun, L.M. Carracedo, R.D. Traub, M.A. Whittington, and N. Kopell, Rhythm generation through period concatenation in rat somatosensory cortex. PLoS Comput. Biol., 2008;4(9):e1000169. PMID: 18773075

M.A. Kramer, R.D. Traub, and N. Kopell, New dynamics in cerebellar Purkinje cells: Torus canards. Phys. Rev. Lett., 2008;101(6):068103. PMID: 18764509

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., 2008; 7(4):1582-611.

S. Middleton. J. Jalics, T. Kispersky, F.E.N. LeBeau, A.K. Roopun, N. Kopell, M.A. Whittington, and M.O. Cunningham, NMDA receptor-dependent switching between different gamma rhythm-generating microcircuits in entorhinal cortex. Proc. Natl. Acad. Sci. U. S. A., 2008; 105(47):18572-7. PMID: 18997013

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;105(46):18023-8. PMID: 19004759

A.K. Roopun, M.A. Kramer, L. Carracedo, M. Kaiser, C. Davies, R.D. Traub, N. Kopell, and M.A. Whittington, Temporal interactions between cortical rhythms. Front. Neurosci., 2008;2(2):145-54. PMID: 19225587

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;1-18.

C.D. Behn, E. Brown, T. Scammell, and N. Kopell, A mathematical model of network dynamics governing mouse sleep-wake behavior. J. Neurophysiol., 2007;97:3828-40. PMID: 17409167

J. Beshel, N. Kopell and L. Kay, Olfactory bulb gamma oscillations are enhanced with task demands. J. Neurosci., 2007;27(31):8358-65. PMID: 17670982

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. PNAS, 2007;104(33):13490-5. PMID: 17679692

R. Silver, K. Boahen, S. Grillner, N. Kopell, K. L. Olsen, Neurotech for neuroscience: Unifying concepts, organizing principles, and emerging tools. J. Neurosci., 2007; 27(44):11807-19. PMID: 17978017

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. PNAS, 2007;104(44):17530-5. PMID: 17954918

S.R. Jones and N. Kopell, Local network parameters can affect inter-network phase lags in central pattern generators. J. Math. Biol., 2006;52:115-40. PMID: 16195924

E. Sivan and N. Kopell, Oscillations and slow patterning in the antennal lobe. J. Comput. Neurosci., 2006;20:85-96. PMID: 16511657

A. Kuznetsov, N. Kopell and C. Wilson, Transient high-frequency firing in a coupled-oscillator model of the mesencephalic dopaminergic neuron. J. Neurophysiol., 2006;95:932-47. PMID: 16207783

H. Rotstein, T. Oppermann, J. White, and N. Kopell, The dynamic structure underlying subthreshold oscillatory activity and the onset of spikes in a model of medial entorhinal cortex stellate cells. J. Comput. Neurosci., 2006;21:271-92. PMID: 16927211

G. Soto, N. Kopell and K. Sen, Network architecture, receptive fields, and neuromodulation: Computational and functional implications of cholinergic modulation in primary auditory cortex. J. Neurophysiol., 2006;96:2972-83. PMID: 16899641

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 state. PNAS, 2006;103:5597-601. PMID: 16565217

D. Pervouchine, T. Netoff, H. Rotstein, J.A. White, M.O. Cunnigham, M.A. Whittington, and N.J. Kopell, Low dimensional maps encoding dynamics in the entorhinal cortex and hippocampus. Neural Comput., 2006;18:2617-50 . PMID: 16999573

T. Netoff, M. Banks, A. Dorval, C. Acker, J. Haas, N. Kopell, and J. White, Synchronization in hybrid neuronal networks of the hippocampal formation. J. Neurophysiol., 2005;93:1197-208. PMID: 15525802

C. Borgers and N. Kopell, Effects of noisy drive on rhythms in networks of excitatory and inhibitory neurons. Neural Comput., 2005;17:557-608. PMID: 15802007

N. Kopell, Biased random walk: A brief mathematical Biography. In Complexities: Women in mathematics, Princeton University Press, 2005;349-54.

O. Jensen, P. Goel, N. Kopell, M. Pohja, R. Hari, B., Ermentrout, On the human sensorimotor-cortex beta rhythm: Sources and modeling. NeuroImage, 2005;26:3347-55. PMID: 15907295

S. Kunec, M.E. Hasselmo and N. Kopell, Encoding and retrieval in the CA3 region of the hippocampus: A model of theta phase separation. J Neurophysiol., 2005;94:70-82. PMID: 15728768

H.G. Rotstein, D.D. Pervouchine, C.D. Acker, M.J. Gillies, J.A. White, E.H. Buhl, M.A. Whittington, and N. Kopell, Slow and fast inhibition and an H-current interact to create a theta rhythm in a model of CA1 interneuron network. J. Neurophysiol., 2005;94:1509-18. PMID: 15857967

R. Clewley, H.G. Rotstein and N. Kopell, A computational tool for the reduction of nonlinear ODE systems possessing multiple scales. Multiscale Modeling and Simulation, 2005;4:732-59.

N. Kopell, Does it have to be so complicated? Editorial Focus on: "Single-column thalamocortical network model exhibiting gamma oscillations, spindles and epileptogenic bursts." J. Neurophysiol., 2005;93:1829-30. PMID: 15774709

C. Borgers, S. Epstein and N.J. Kopell, Background gamma rhythmicity and attention in cortical local circuits: A computational study. Proc. Nat. Acad. Sci. U.S. A., 2005;102:7002-7. PMID: 15870189

T. Gloveli, T. Dugladze, H.G. Rotstein, R.D. Traub, H. Monyer, U. Heinemann, M.A. Whittington, and N.J. Kopell, Orthogonal arrangement of rhythm-generating microcircuits in the hippocampus. Proc. Nat. Acad. Sci. U. S. A., 2005;102:13295-300. PMID: 16141320

N. Kopell and B. Ermentrout, Chemical and electrical synapses perform complementary roles in the synchronization of interneuronal networks. Proc. Nat. Acad. Sci. U.S.A., 2004;101:15482-7. PMID: 15489269

E. Sivan and N. Kopell, Mechanism and circuitry for clustering and fine discrimination of odors in insects. Proc. Nat. Acad. Sci. U.S.A., 2004;101:17861-6. PMID: 15590772

A. Kuznetsov, M. Kaern and N. Kopell, Synchrony in a population of hysteresis-based genetic oscillators. SIAM J. Appl. Math., 2004; 65:392-425.

M. Olufsen, M.A. Whittington, M. Camperi, and N. Kopell, New roles for the gamma rhythm: Population tuning and preprocessing for the Beta rhythm. J. Comput. Neurosci., 2003;14:35-54. PMID: 12435923

C. Borgers and N. Kopell, Synchronization in network of excitatory and inhibitory neurons with sparse, random connectivity. Neural Comput., 2003;15:509-38. PMID: 12620157

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. Comput. Neurosci., 2003;15:283-98.

S.R. Jones, B. Mulloney, T. Kaper, and N. Kopell, Coordination of cellular pattern-generating circuits that control limb movements: The sources of stable differences in intersegmental phases. J. Neurosci., 2003;23:3457-68. PMID: 12716954

C. Acker, N. Kopell and J. White, Synchronization of strongly coupled excitatory neurons: relating network behavior to biophysics. J. Comput. Neurosci., 2003;15: 71-90. PMID: 12843696

H.G. Rotstein, N. Kopell, A.M. Zhabotinsky, and I.R. Epstein, A canard mechanism in systems of globally coupled oscillators. SIAM J. Appl. Math., 2003;63:1998-2019.

G. Medvedev, C. Wilson, J. Callaway, and N. Kopell, Dendritic synchrony and transient dynamics in a coupled oscillator model of the dopaminergic neuron. J. Comput. Neurosci., 2003;15:53-69. PMID: 12843695

D. McMillen and N.Kopell, Noise-stabilized synchronization in populations of model neurons. J. Comput. Neurosci., 2003;15:143-57. PMID: 14512745

N.S. Sung, J. Gordon, G. Rose, E. Getzoff, S. Kron, D. Mumford, J. Onuchic, N. Scherer, D.L. Sumners, and N.J.Kopell, Science education. Education future scientists. Science, 2003;301: 1485. PMID: 12970550

BIO 2010: Transforming undergraduate education for future research scientists. Committee on undergraduate biology education to prepare research scientists for the 21st century, National Research Council, the National Academies Press, Washington, D.C., 2003.

N. Kopell, A tree of fireflies, a flock of boson clouds. Review of Sync by S.Strogatz, Science, 2003;300:878-9.

M.O. Cunningham, C.H. Davies, E.H. Buhl, N. Kopell, and M.A. Whittington, Gamma oscillations induced by kainate receptor activation in the entorhinal cortex in vitro. J. Neurosci., 2003;23:9761-9. PMID: 14586003

H.G. Rotstein, N. Kopell, A.M. Zhabotinsky, and I.R. Epstein, Canard phenomenon and localization of oscillations in the Belousov-Zhabotinsky reaction with global feedback. J. Chemical Physics, 2003;119:8824-32.

N. Kopell, Rhythms in the nervous system: From cells to behavior via dynamics. In Proc. of Internat. Congress of Industrial and Appl. Math, Sydney, Australia, 2003.

L. Rubchinsky, N. Kopell and K. Sigvardt, Modeling facilitation and inhibition of competing motor programs in basal ganglia subthalamic nucleus-pallidal circuits. Proc. Natl. Acad. Sci. U. S. A., 2003;100:14427-32. PMID: 14612573

N. Kopell and G.B. Ermentrout, Chains of coupled oscillators in motor and sensory systems. In Handbook of brain theory and neural networks, M. Arbib, ed., MIT Press, Cambridge, MA, 2002.

N. Kopell and G.B. Ermentrout, Mechanisms of phase-locking and frequency control in pairs of coupled neural oscillators. In Handbook on dynamical systems, volume 2: Toward applications, B. Fiedler, ed., Elsevier, Philadelphia, 2002;3-54.

D. McMillen, N. Kopell, J. Hasty, and J.J. Collins, Synchronizing genetic relaxation oscillators by intercell signaling. Proc. Nat. Acad. Sci. U.S.A., 2002;99:679-84. PMID:11805323

O. Jensen, M. Pohja, P. Goel, G.B. Ermentrout, N. Kopell, and R. Hari, On the physiological basis of the 15-30 Hz motor-cortex rhythm. Proc. of 13th Int. Conf. on Biomagnetism, 2002.

N. Kopell, Rhythms of the nervous system: Mathematical themes and variations. Proc. of the Int. Congress of Mathematicians, Beijing 2002, Springer, 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 oscillation. Proc. Nat. Acad. Sci. U. S. A., 2001;98:3571-6. PMID: 11248119

G. Medvedev and N. Kopell, Synchronization and transient dynamics in chains of FitzHugh Nagumo oscillators with strong electrical coupling. SIAM J. Appl. Math., 2001;61:1762-1801.

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., 2001;21:9478-86. PMID: 11717382

N. Kopell, G.B. Ermentrout, M. Whittington, and R.D. Traub, Gamma rhythms and beta rhythms have different synchronization properties. Proc. Nat. Acad. Sci. U. S. A., 2000;97:1867-72. PMID: 10677548

A. Bose, N. Kopell, D. Terman, Almost synchronous solutions for pairs of neurons coupled by excitation. Physica D, 2000;140:69-94.

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, 2000;47:6-16.

G. Medvedev, T. Kaper and N. Kopell, A reaction-diffusion system with periodic front dynamics. SIAM J. Appl. Math., 2000;60:1601-38.

J. Karbowski and N. Kopell, Multispikes and synchronization in a large neural network with temporal delays. Neural Comput., 2000;12:1573-1606. PMID: 10935919

C. Chow and N. Kopell, Dynamics of spiking neurons with electrical coupling. Neural Comput., 2000;12:1643-78. PMID: 10935921

M.A. Whittington, R.D. Traub, N. Kopell, B. Ermentrout, and E.H. Buhl, Inhibition-based rhythms: Experimental and mathematical observation on network dynamics. Int. J. of Psychophysiol., 2000;38:315-36. PMID: 11102670

J. White, M. Banks, R. Pearce, and N. Kopell, Networks of interneurons with fast and slow gamma-aminobutyric acid type A (GABAA) kinetics provide substrate for mixed gamma-theta rhythm. Proc. Nat. Acad. Sci. U. S. A., 2000;97:8128-33. PMID: 10869419

S. R. Jones, D. Pinto, T. Kaper, and N. Kopell, Alpha-frequency rhythms desynchronize over long cortical distances: A modeling study. J. Comput. Neurosci., 2000;9:271-91. PMID: 11139043

Y. Manor, F. Nadim, S. Epstein, J. Ritt, E. Marder, N. Kopell, Network oscillations generated by balancing graded asymmetric reciprocal inhibition in passive neurons. J. Neurosci., 1999;19:1765-2779. PMID: 10087088

T. LoFaro and N. Kopell, Timing regulation in a network reduced from voltage-gated equations to a one-dimensional map. J. Math. Biol., 1999;38:479-533. PMID: 10422266

F. Nadim, Y. Manor, N. Kopell, and E. Marder, Synaptic depression creates a switch that controls the frequency of an oscillatory circuit. Proc. of Nat Acad. Sci. U. S. A., 1999;96:8206-11. PMID: 10393973

E. Marder, N. Kopell and K. Sigvardt, How computation aids in understanding biological networks. In Neurons, networks and motor behavior, P.S.G. Stein, S. Grillner, A.I. Selverston, and D.G. Stuart, eds., MIT Press, Cambridge, MA, 1998;139-50.

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. Intl. J. Bifurcations and Chaos, 1998;8:189-209.

J. White, C. Chow, J. Ritt, C. Soto-Trevino, and N. Kopell, Synchronization and oscillatory dynamics in heterogeneous, mutually inhibited neurons. J. Comput. Neurosci., 1998;5:5-16. PMID: 9580271

G.B. Ermentrout and N. Kopell, Fine structure of neural spiking and synchronization in the presence of conduction delays. Proc. Nat. Acad. Sci. U. S. A., 1998;95:1259-64. PMID: 9448319

D. Terman, A. Bose, and N. Kopell, Dynamics of two mutually coupled slow inhibitory neurons. Physica D, 1998;117:241-75. [Abstract HTML] [Preprint PDF]

N. Kopell, L. Abbott and C. Soto-Trevino, On the behavior of a neural oscillator electrically coupled to a bistable element. Physica D, 1998;121:367-95.

C. Chow, J. White, J. Ritt, and N. Kopell, Frequency control in synchronized networks of inhibitory neurons. J. Comput. Neurosci., 1998;5:407-20. PMID: 9877022

N. Kopell, Networks of neurons as dynamical systems: From geometry to biophysics. Quarterly Appl. Math., 1998;56:707-18.

N. Kopell, Oscillating networks of neurons: Mathematics and function. In Proc. of The legacy of Norbert Wiener: A centennial symposium, American Mathematical Society, Providence, 1997.

J.M. Weimann, P. Skiebe, H. Heinzel, C. Soto, N. Kopell, J.C. Jorge-Rivera, and E. Marder, Modulation of oscillator interactions in the crab stomatogastric ganglion by crustacean cardioactive peptide. J. Neurosci., 1997;17:1748-60. PMID: 9030633

F. Skinner, N. Kopell and B. Mulloney, How does the crayfish swimmeret system work: Insights from nearest-neighbor coupled oscillator models. J. Comp. Neurosci., 1997;4:151-60.

N. Kopell, Global center manifolds and singularly perturbed equations. A brief guide to the literature. In Lectures in applied math, American Mathematical Society, Providence, 1996;31:47-50.

C. Jones, T. Kaper and N. Kopell, Tracking invariant manifolds up to exponentially small errors. SIAM J. Math. Anal., 1996;27:558-77.

C. Soto-Trevino, N. Kopell and D. Watson, Parabolic bursting revisited. J. Math. Biol., 1996;35:114-28. PMID: 9002243

D. Terman, A. Bose and N. Kopell, Functional reorganization in thalamocortical networks: Transition between spindling and delta sleep rhythms. Proc. Nat. Acad. Sci. U. S. A., 1996;93:15417-22. PMID: 8986826

N. Kopell and D. Somers, Anti-phase solutions in relaxation oscillators coupled through excitatory interactions. J. Math. Biol., 1995;33:261-80. PMID: 7897329

N. Kopell, Chains of coupled oscillators. In Handbook of brain theory and neural networks, M. Arbib, ed., MIT Press, Cambridge, 1995;178-83.

N. Kopell and M. Landman, Spatial structure of the focusing singularity of the nonlinear Schrodinger equation: A geometric analysis. SIAM J. Appl. Math., 1995;55:1297-323.

D. Somers and N. Kopell, Waves and synchrony in arrays of oscillators of relaxation and non-relaxation type. Physica D, 1995;89:169-83.

University Lecture, Boston University, Boston MA, 1994.

C. Jones and N. Kopell, Tracking invariant manifolds with differential forms in singularly perturbed equations. J. Diff. Equa., 1994;108:64-88.

T. LoFaro, N. Kopell, E. Marder, and S. Hooper, Subharmonic coordination in networks of neurons with slow conductances. Neural Computation, 1994;6:69-84.

G.B. Ermentrout and N. Kopell, Inhibition-produced patterning in chains of coupled nonlinear oscillators. SIAM J. Appl. Math., 1994;54:478-507.

G.B. Ermentrout and N. Kopell, Learning of phase-lags in coupled neural oscillators. Neural Computation, 1994;6:225-41.

F. Skinner, N. Kopell and E. Marder, Mechanisms for oscillation and frequency control in networks of mutually inhibitory relaxation oscillators. J. Computational Neuroscience, 1994;1:69-87. PMID: 8792226

F. Skinner, S. Gramoll, R. Calabrese, N. Kopell, and E. Marder, Frequency control in biological half-center oscillators. In Computations in neurons and neural systems, F.H. Eeckman, ed., Kluwer, Boston, 1994;223-8.

T. LoFaro, N. Kopell, E. Marder, and S. Hooper, The effect of i_h bursting patterns of pairs of coupled neurons. In Computations in neurons and neural systems, F.H. Eeckman, ed., Kluwer, Boston, 1994;15-20.

N. Kopell and G. LeMasson, Rhythmogenesis, amplitude modulation and multiplexing in a cortical architecture. Proc. Nat. Acad. Sci. U.S.A., 1994;91:10586-90. PMID: 7937997

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), 1994;31:1558-76.

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.

D. Somers and N. Kopell, Rapid synchronization through fast threshold modulation. Biol. Cybern., 1993;68:393-407. PMID: 8476980

E. Marder, L. Abbott, A. Sharp, and N. Kopell, Electrical coupling in networks containing oscillators. In Neuroscience: From neural networks to artificial intelligence,

Research notes in neural computing, M. Arbib, P. Rudomin, and F. Cervantes, eds., Springer Verlag, New York, 1993;33-42.

N. Kopell, Rhythms and clues: Mechanisms of self-organization in nature, 1993

A.H. Cohen, G.B. Ermentrout, T. Kiemel, N. Kopell, K. Sigvardt, and T. Williams, Modeling of intersegmental coordination in the lamprey central pattern generator for locomotion. Trends in Neurosciences, 1992;15:434-438. PMID: 1281350

G.B. Ermentrout and N. Kopell, Multiple pulse interactions and averaging in coupled neural oscillators. Journal of Math. Biol., 1991;29:195-217.

N. Kopell, G.B. Ermentrout and Thelma Williams, On chains of neural oscillators forced at one end. SIAM J. Appl. Math., 1991;51:1397-17.

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, H. Swinney, G. Aris and D. Aronson, eds., Springer-Verlag, New York, 1991;37:101-16.

N. Kopell and G.B. Ermentrout, Structure and function in an oscillating neural network. In Computational neuroscience, E. Schwartz, ed., MIT Press, Boston, 1990;201-9.

G.B. Ermentrout and N. Kopell, Oscillator death in systems of coupled neural oscillators. SIAM J. Appl. Math., 1990;50:125-46.

N. Kopell and G.B. Ermentrout, Phase transitions and other phenomena in chains of oscillators. SIAM J. Appl. Math., 1990;50:1014-52.

D.G. Aronson, G.B. Ermentrout and N. Kopell, Amplitude response of coupled oscillators. Physica D, 1990;41:403-49.

N. Kopell, W. Zhang and G.B. Ermentrout, Multiple coupling in chains of oscillators. SIAM J. Math. Anal., 1990;21:935-53.

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. Journal of Neurophysiology, 1990;64:862-71. PMID: 2230930

G.B. Ermentrout and N. Kopell, Some mathematical questions concerning central pattern generators. In Theoretical models of cell signaling, A. Goldbeter, ed., Academic Press, New York, 1989;89-98.

N. Kopell and G.B. Ermentrout, Coupled oscillators and the design of central pattern generators. Math. Biosciences, 1988;90:87-109.

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.

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.

G.B. Ermentrout and N. Kopell, Parabolic bursting in an excitable system coupled with a slow oscillation. SIAM J. Appl. Math., 1986;46:233-53.

N. Kopell and G.B. Ermentrout, Subcellular oscillations and bursting. Math. Biosciences, 1986;78:265-91.

N. Kopell and D. Ruelle, Bounds on complexity in reaction-diffusion systems. SIAM J. Appl. Math., 1986;46:68-80.

N. Kopell, Phase methods for coupled oscillators and related topics: An annotated bibliography. J. Statistical Physics, 1986;44:1035-42.

N. Kopell, Coupled oscillators and locomotion by fish. In Nonlinear oscillations in biology and chemistry, H. Othmer, ed., Lecture Notes in Biomathematics, Springer-Verlag, New York, 1986;66:166-74.

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, Macmillan, London, 1986;45:383-5.

N. Kopell and G.B. Ermentrout, Symmetry and phaselocking in chains of weakly coupled oscillators. Comm. Pure Appl. Mathematics, 1986;39:623-60.

N. Kopell, Invariant manifolds and the initialization problem for some atmospheric equations. Physica D, 1985;14:203-15.

G.B. Ermentrout and N. Kopell, Frequency plateaus in a chain of weakly coupled oscillators. SIAM J. on Math. Anal., 1984;15:215-37.

N. Kopell, Forced and coupled oscillators in biological applications. Proc. of the 1983 International Congress, Warsaw, North Holland, Amsterdam, 1984;1645-60.

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 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, 1982;11:738-46.

N. Kopell, Frequency plateaus in a chain of weakly coupled oscillators. In Nonlinear partial differential equations, Contemporary Mathematics, J. Smoller, ed., American Mathematical Society, Providence, 1982;17:401-4. (This is an exposition of the ideas in 25.)

N. Kopell and G.B. Ermentrout, Coupled oscillators and mammalian small intestines. In Oscillation in mathematical biology, Lecture Notes in Biomathematics, J.P.E. Hodgson, ed., Springer-Verlag, New York, 1982;51:24-36.

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., 1981;64:1-56.

N. Kopell and S. Parter, A complete analysis of a model nonlinear equation having a continuous locus of turning points. Advances in Appl. Math., 1981;2:212-38.

N. Kopell and L.N. Howard, Target patterns and spiral solutions to reaction-diffusion equations with more than one space dimension. Adv. Appl. Math., 1981;2:417-49.

N. Kopell, Target pattern solutions to reaction-diffusion equations in the presence of impurities. Adv. Appl. Math., 1981;2:389-99.

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; 173-90.

N. Kopell, A geometric approach to boundary layer problems exhibiting resonance. SIAM J. Appl. Math, 1979;37:436-58.

L.N. Howard and N. Kopell, Translation, with editorial comments, of E. Hopf's Abzeigung einer periodischen Losung von einer stationaren Losung eines Differentialsystems. In The Hopf Bifurcation and its Applications, Applied Mathematical Sciences, J. Marsden and M. McCracken, eds., Springer-Verlag, New York, 1978;19: 163-205.

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, 1978;15:191-205.

L.N. Howard and N. Kopell, Slowly varying waves and shocks in reaction-diffusion equations. Studies in Appl. Math., 1977;56:95-145.

N. Kopell, Waves, shocks and target patterns in an oscillating chemical reagent. In Nonlinear Diffusion, Research Notes in Mathematics, 1977;14:129-54, Pitman.

N. Kopell and L.N. Howard, Bifurcations and trajectories joining critical points. Adv. in Math., 1975;18:306-58.

N. Kopell and G. Stolzenberg, Commentary on Bishop's talk. Historia Mathematica, 1975;2:519-21.

N. Kopell, Discussion paper: Dissipative and non-dissipative structure. Ann. of the N.Y. Acad. Sciences, 1974;231:106-7. PMID: 4522887

N. Kopell and L.N. Howard, Bifurcation under non-generic conditions. Adv. in Math., 1974;13:274-83.

N. Kopell and L.N. Howard, Pattern formation in the Belousov reaction. Lectures on Mathematics in the Life Sciences, 1974:7:201-16.

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, American Mathematical Society, Providence, 1974;8:274-83.

N. Kopell and L.N. Howard, Horizontal bands in the Belousov reaction. Science, 1973; 180:1171-3. PMID: 17743601

N. Kopell and L.N. Howard, Plane wave solutions to reaction diffusion equations. Studies in Appl. Math., 1973;52:291-328.

N. Kopell, Commuting diffeomorphisms. In Global Analysis, Symposia in Pure Mathematics, American Mathematical Society, Providence, 1970;14:165-84.