Keywords
Last Name

Nancy Kopell, PhD

TitleProfessor
InstitutionBoston University College of Arts and Sciences
DepartmentMathematics and Statistics
Address111 Cummington St
Boston MA 02215
Phone(617) 353-5210
ORCID ORCID Icon0000-0002-8568-8750
Other Positions
TitleCo-Director
InstitutionBoston University
DepartmentCenter for Computational Neuroscience & Neural Technology

TitleProfessor
InstitutionBoston University School of Medicine
DepartmentPharmacology & Experimental Therapeutics

 Awards and Honors

Start-EndDescription
1996-presNational Academy of Sciences: Member
1996-presAmerican Academy of Arts and Sciences: Member
2011-presLondon Mathematical Society: Honorary Member
2009SIAM: Fellow
2008Massachusetts Academy of Sciences: Fellow
2006Oxford University: Weldon Memorial Prize
2006New Jersey Institute of Technology: Honorary Doctorate
1990-1995John D. and Catherine T. MacArthur Fellow
1984-1985J. S. Guggenheim Fellowship
1975-1977Alfred P. Sloan Fellow
1963-1967N.S.F. Graduate Fellow
1963-1964Woodrow Wilson Fellow (honorary)
 Research Expertise & Professional Interests
Nancy Kopell received her B.A. from Cornell University in 1963 and her Ph.D. from Berkeley in 1967. She is currently the William Fairfield Warren Distinguished Professor at Boston University, and co-director of the Center for Computational Neuroscience and Neural Technology (CompNet). She organized and directs the Cognitive Rhythms Collaborative (CRC), a group of over two dozen labs, mostly in the Boston Area, working on brain dyanmics and their cognitive implications.

Kopell's Ph.D. training was in pure mathematics, but she transitioned to applied mathematics shortly after receiving her degree. In the first part of her career, she worked on pattern formation in chemical systems, oscillating systems and problems involving the geometry of systems with multiple time scales. For the last two decades, she has worked on mathematical problems in neuroscience. Her current interests parallel the themes of the CRC: how does the brain produce its dynamics (physiological mechanisms), how do brain rhythms take part in cognition (sensory processing, attention, memory, motor control), and how can pathologies of brain dynamics help to understand symptoms of neurological diseases (Parkinson's disease, schizophrenia, epilepsy) as well as alternate states of consciousness (anesthesia). She collaborates widely with experimentalists and clinicians.

Kopell is a member of the National Academy of Sciences and the American Academy of Arts and Sciences. She was recently selected to be an honorary member of the London Mathematical Society, a distinction given to one or two mathematicians per year worldwide. She has been awarded Sloan Guggenheim, and McArthur Fellowships, and has an honory Ph.D. from the New Jersey Institute of Technology. She has given the Weldon Memorial Prize Lecture (Oxford), the von Neumann Lecture (SIAM) and the Josiah Willard Gibbs Lecture (AMS, as well as multiple other named lectureships.

 Publications
Publications listed below are automatically derived from MEDLINE/PubMed and other sources, which might result in incorrect or missing publications. Faculty can login to make corrections and additions.
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  1. Kondabolu K, Roberts EA, Bucklin M, McCarthy MM, Kopell N, Han X. Striatal cholinergic interneurons generate beta and gamma oscillations in the corticostriatal circuit and produce motor deficits. Proc Natl Acad Sci U S A. 2016 May 31; 113(22):E3159-68. PMID: 27185924.
    View in: PubMed
  2. Ainsworth M, Lee S, Kaiser M, Simonotto J, Kopell NJ, Whittington MA. GABAB receptor-mediated, layer-specific synaptic plasticity reorganizes gamma-frequency neocortical response to stimulation. Proc Natl Acad Sci U S A. 2016 May 10; 113(19):E2721-9. PMID: 27118845.
    View in: PubMed
  3. Scholvin J, Kinney JP, Bernstein JG, Moore-Kochlacs C, Kopell N, Fonstad CG, Boyden ES. Close-Packed Silicon Microelectrodes for Scalable Spatially Oversampled Neural Recording. IEEE Trans Biomed Eng. 2016 Jan; 63(1):120-30. PMID: 26699649.
    View in: PubMed
  4. Lee JH, Whittington MA, Kopell NJ. Potential Mechanisms Underlying Intercortical Signal Regulation via Cholinergic Neuromodulators. J Neurosci. 2015 Nov 11; 35(45):15000-14. PMID: 26558772.
    View in: PubMed
  5. Cannon J, Kopell N, Gardner T, Markowitz J. Neural Sequence Generation Using Spatiotemporal Patterns of Inhibition. PLoS Comput Biol. 2015 Nov; 11(11):e1004581. PMID: 26536029.
    View in: PubMed
  6. Kinney JP, Bernstein JG, Meyer AJ, Barber JB, Bolivar M, Newbold B, Scholvin J, Moore-Kochlacs C, Wentz CT, Kopell NJ, Boyden ES. A direct-to-drive neural data acquisition system. Front Neural Circuits. 2015; 9:46. PMID: 26388740.
    View in: PubMed
  7. Vijayan S, Klerman EB, Adler GK, Kopell NJ. Thalamic mechanisms underlying alpha-delta sleep with implications for fibromyalgia. J Neurophysiol. 2015 Sep; 114(3):1923-30. PMID: 26245315.
    View in: PubMed
  8. Pittman-Polletta BR, Kocsis B, Vijayan S, Whittington MA, Kopell NJ. Brain rhythms connect impaired inhibition to altered cognition in schizophrenia. Biol Psychiatry. 2015 Jun 15; 77(12):1020-30. PMID: 25850619.
    View in: PubMed
  9. Santaniello S, McCarthy MM, Montgomery EB, Gale JT, Kopell N, Sarma SV. Therapeutic mechanisms of high-frequency stimulation in Parkinson's disease and neural restoration via loop-based reinforcement. Proc Natl Acad Sci U S A. 2015 Feb 10; 112(6):E586-95. PMID: 25624501.
    View in: PubMed
  10. Kopell NJ, Gritton HJ, Whittington MA, Kramer MA. Beyond the connectome: the dynome. Neuron. 2014 Sep 17; 83(6):1319-28. PMID: 25233314.
    View in: PubMed
  11. Börgers C, Li J, Kopell N. Approximate, not Perfect Synchrony Maximizes the Downstream Effectiveness of Excitatory Neuronal Ensembles. J Math Neurosci. 2014 Dec; 4(1):10. PMID: 27334376.
    View in: PubMed
  12. Cannon J, McCarthy MM, Lee S, Lee J, Börgers C, Whittington MA, Kopell N. Neurosystems: brain rhythms and cognitive processing. Eur J Neurosci. 2014 Mar; 39(5):705-19. PMID: 24329933.
    View in: PubMed
  13. Devor A, Bandettini PA, Boas DA, Bower JM, Buxton RB, Cohen LB, Dale AM, Einevoll GT, Fox PT, Franceschini MA, Friston KJ, Fujimoto JG, Geyer MA, Greenberg JH, Halgren E, Hämäläinen MS, Helmchen F, Hyman BT, Jasanoff A, Jernigan TL, Judd LL, Kim SG, Kleinfeld D, Kopell NJ, Kutas M, Kwong KK, Larkum ME, Lo EH, Magistretti PJ, Mandeville JB, Masliah E, Mitra PP, Mobley WC, Moskowitz MA, Nimmerjahn A, Reynolds JH, Rosen BR, Salzberg BM, Schaffer CB, Silva GA, So PT, Spitzer NC, Tootell RB, Van Essen DC, Vanduffel W, Vinogradov SA, Wald LL, Wang LV, Weber B, Yodh AG. The challenge of connecting the dots in the B.R.A.I.N. Neuron. 2013 Oct 16; 80(2):270-4. PMID: 24139032.
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  14. Dugladze T, Maziashvili N, Börgers C, Gurgenidze S, Häussler U, Winkelmann A, Haas CA, Meier JC, Vida I, Kopell NJ, Gloveli T. GABA(B) autoreceptor-mediated cell type-specific reduction of inhibition in epileptic mice. Proc Natl Acad Sci U S A. 2013 Sep 10; 110(37):15073-8. PMID: 23980149.
    View in: PubMed
  15. Mitry J, McCarthy M, Kopell N, Wechselberger M. Excitable neurons, firing threshold manifolds and canards. J Math Neurosci. 2013; 3(1):12. PMID: 23945278.
    View in: PubMed
  16. Lee JH, Whittington MA, Kopell NJ. Top-down beta rhythms support selective attention via interlaminar interaction: a model. PLoS Comput Biol. 2013; 9(8):e1003164. PMID: 23950699.
    View in: PubMed
  17. Vijayan S, Ching S, Purdon PL, Brown EN, Kopell NJ. Thalamocortical mechanisms for the anteriorization of a rhythms during propofol-induced unconsciousness. J Neurosci. 2013 Jul 3; 33(27):11070-5. PMID: 23825412.
    View in: PubMed
  18. Kopell N. Interview with Nancy Kopell. Trends Neurosci. 2013 Jun; 36(6):313-4. PMID: 23731518.
    View in: PubMed
  19. Purdon PL, Pierce ET, Mukamel EA, Prerau MJ, Walsh JL, Wong KF, Salazar-Gomez AF, Harrell PG, Sampson AL, Cimenser A, Ching S, Kopell NJ, Tavares-Stoeckel C, Habeeb K, Merhar R, Brown EN. Electroencephalogram signatures of loss and recovery of consciousness from propofol. Proc Natl Acad Sci U S A. 2013 Mar 19; 110(12):E1142-51. PMID: 23487781.
    View in: PubMed
  20. Vijayan S, Ching S, Purdon PL, Brown EN, Kopell NJ. Biophysical Modeling of Alpha Rhythms During Halothane-Induced Unconsciousness. Int IEEE EMBS Conf Neural Eng. 2013; 1104-1107. PMID: 25284633.
    View in: PubMed
  21. Vijayan S, Kopell NJ. Thalamic model of awake alpha oscillations and implications for stimulus processing. Proc Natl Acad Sci U S A. 2012 Nov 6; 109(45):18553-8. PMID: 23054840.
    View in: PubMed
  22. Ainsworth M, Lee S, Cunningham MO, Traub RD, Kopell NJ, Whittington MA. Rates and rhythms: a synergistic view of frequency and temporal coding in neuronal networks. Neuron. 2012 Aug 23; 75(4):572-83. PMID: 22920250.
    View in: PubMed
  23. Malerba P, Kopell N. Phase resetting reduces theta-gamma rhythmic interaction to a one-dimensional map. J Math Biol. 2013 Jun; 66(7):1361-86. PMID: 22526842.
    View in: PubMed
  24. McCarthy MM, Ching S, Whittington MA, Kopell N. Dynamical changes in neurological diseases and anesthesia. Curr Opin Neurobiol. 2012 Aug; 22(4):693-703. PMID: 22446010.
    View in: PubMed
  25. Munro E, Kopell N. 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 May; 107(10):2833-52. PMID: 22378167.
    View in: PubMed
  26. Börgers C, Talei Franzesi G, Lebeau FE, Boyden ES, Kopell NJ. Minimal size of cell assemblies coordinated by gamma oscillations. PLoS Comput Biol. 2012 Feb; 8(2):e1002362. PMID: 22346741.
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  27. Ching S, Purdon PL, Vijayan S, Kopell NJ, Brown EN. A neurophysiological-metabolic model for burst suppression. Proc Natl Acad Sci U S A. 2012 Feb 21; 109(8):3095-100. PMID: 22323592.
    View in: PubMed
  28. Ainsworth M, Lee S, Cunningham MO, Roopun AK, Traub RD, Kopell NJ, Whittington MA. Dual ? rhythm generators control interlaminar synchrony in auditory cortex. J Neurosci. 2011 Nov 23; 31(47):17040-51. PMID: 22114273.
    View in: PubMed
  29. Tort AB, Komorowski R, Kopell N, Eichenbaum H. A mechanism for the formation of hippocampal neuronal firing patterns that represent what happens where. Learn Mem. 2011; 18(11):718-27. PMID: 22021254.
    View in: PubMed
  30. McCarthy MM, Moore-Kochlacs C, Gu X, Boyden ES, Han X, Kopell N. Striatal origin of the pathologic beta oscillations in Parkinson's disease. Proc Natl Acad Sci U S A. 2011 Jul 12; 108(28):11620-5. PMID: 21697509.
    View in: PubMed
  31. Kopell N, Whittington MA, Kramer MA. Neuronal assembly dynamics in the beta1 frequency range permits short-term memory. Proc Natl Acad Sci U S A. 2011 Mar 1; 108(9):3779-84. PMID: 21321198.
    View in: PubMed
  32. Desai M, Kahn I, Knoblich U, Bernstein J, Atallah H, Yang A, Kopell N, Buckner RL, Graybiel AM, Moore CI, Boyden ES. Mapping brain networks in awake mice using combined optical neural control and fMRI. J Neurophysiol. 2011 Mar; 105(3):1393-405. PMID: 21160013.
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  33. Ching S, Cimenser A, Purdon PL, Brown EN, Kopell NJ. Thalamocortical model for a propofol-induced alpha-rhythm associated with loss of consciousness. Proc Natl Acad Sci U S A. 2010 Dec 28; 107(52):22665-70. PMID: 21149695.
    View in: PubMed
  34. Kopell N, Kramer MA, Malerba P, Whittington MA. Are different rhythms good for different functions? Front Hum Neurosci. 2010; 4:187. PMID: 21103019.
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  35. Tort AB, Komorowski R, Eichenbaum H, Kopell N. Measuring phase-amplitude coupling between neuronal oscillations of different frequencies. J Neurophysiol. 2010 Aug; 104(2):1195-210. PMID: 20463205.
    View in: PubMed
  36. Tort AB, Fontanini A, Kramer MA, Jones-Lush LM, Kopell NJ, Katz DB. Cortical networks produce three distinct 7-12 Hz rhythms during single sensory responses in the awake rat. J Neurosci. 2010 Mar 24; 30(12):4315-24. PMID: 20335467.
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  37. Lee S, Sen K, Kopell N. Cortical gamma rhythms modulate NMDAR-mediated spike timing dependent plasticity in a biophysical model. PLoS Comput Biol. 2009 Dec; 5(12):e1000602. PMID: 20011119.
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  38. Brea JN, Kay LM, Kopell NJ. Biophysical model for gamma rhythms in the olfactory bulb via subthreshold oscillations. Proc Natl Acad Sci U S A. 2009 Dec 22; 106(51):21954-9. PMID: 19996171.
    View in: PubMed
  39. Tort AB, Komorowski RW, Manns JR, Kopell NJ, Eichenbaum H. Theta-gamma coupling increases during the learning of item-context associations. Proc Natl Acad Sci U S A. 2009 Dec 8; 106(49):20942-7. PMID: 19934062.
    View in: PubMed
  40. Shamir M, Ghitza O, Epstein S, Kopell N. Representation of time-varying stimuli by a network exhibiting oscillations on a faster time scale. PLoS Comput Biol. 2009 May; 5(5):e1000370. PMID: 19412531.
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  41. Kay LM, Beshel J, Brea J, Martin C, Rojas-Líbano D, Kopell N. Olfactory oscillations: the what, how and what for. Trends Neurosci. 2009 Apr; 32(4):207-14. PMID: 19243843.
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  42. Wulff P, Ponomarenko AA, Bartos M, Korotkova TM, Fuchs EC, Bähner F, Both M, Tort AB, Kopell NJ, Wisden W, Monyer H. 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. PMID: 19204281.
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  43. Roopun AK, Kramer MA, Carracedo LM, Kaiser M, Davies CH, Traub RD, Kopell NJ, Whittington MA. Temporal Interactions between Cortical Rhythms. Front Neurosci. 2008 Dec; 2(2):145-54. PMID: 19225587.
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  44. Tort AB, Kramer MA, Thorn C, Gibson DJ, Kubota Y, Graybiel AM, Kopell NJ. 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 Dec 23; 105(51):20517-22. PMID: 19074268.
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  45. McCarthy MM, Brown EN, Kopell N. Potential network mechanisms mediating electroencephalographic beta rhythm changes during propofol-induced paradoxical excitation. J Neurosci. 2008 Dec 10; 28(50):13488-504. PMID: 19074022.
    View in: PubMed
  46. Börgers C, Epstein S, Kopell NJ. 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. PMID: 19004759.
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  47. Middleton S, Jalics J, Kispersky T, Lebeau FE, Roopun AK, Kopell NJ, Whittington MA, Cunningham MO. NMDA receptor-dependent switching between different gamma rhythm-generating microcircuits in entorhinal cortex. Proc Natl Acad Sci U S A. 2008 Nov 25; 105(47):18572-7. PMID: 18997013.
    View in: PubMed
  48. Kramer MA, Roopun AK, Carracedo LM, Traub RD, Whittington MA, Kopell NJ. Rhythm generation through period concatenation in rat somatosensory cortex. PLoS Comput Biol. 2008; 4(9):e1000169. PMID: 18773075.
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  49. Kramer MA, Traub RD, Kopell NJ. New dynamics in cerebellar Purkinje cells: torus canards. Phys Rev Lett. 2008 Aug 8; 101(6):068103. PMID: 18764509.
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  50. Diniz Behn CG, Kopell N, Brown EN, Mochizuki T, Scammell TE. Delayed orexin signaling consolidates wakefulness and sleep: physiology and modeling. J Neurophysiol. 2008 Jun; 99(6):3090-103. PMID: 18417630.
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  51. Roopun AK, Kramer MA, Carracedo LM, Kaiser M, Davies CH, Traub RD, Kopell NJ, Whittington MA. Period concatenation underlies interactions between gamma and beta rhythms in neocortex. Front Cell Neurosci. 2008; 2:1. PMID: 18946516.
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  52. Krupa M, Popovic N, Kopell N, Rotstein HG. Mixed-mode oscillations in a three time-scale model for the dopaminergic neuron. Chaos. 2008 Mar; 18(1):015106. PMID: 18377087.
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  53. Vierling-Claassen D, Siekmeier P, Stufflebeam S, Kopell N. Modeling GABA alterations in schizophrenia: a link between impaired inhibition and altered gamma and beta range auditory entrainment. J Neurophysiol. 2008 May; 99(5):2656-71. PMID: 18287555.
    View in: PubMed
  54. Kramer MA, Tort AB, Kopell NJ. Sharp edge artifacts and spurious coupling in EEG frequency comodulation measures. J Neurosci Methods. 2008 May 30; 170(2):352-7. PMID: 18328571.
    View in: PubMed
  55. Börgers C, Kopell NJ. Gamma oscillations and stimulus selection. Neural Comput. 2008 Feb; 20(2):383-414. PMID: 18047409.
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  56. Silver R, Boahen K, Grillner S, Kopell N, Olsen KL. Neurotech for neuroscience: unifying concepts, organizing principles, and emerging tools. J Neurosci. 2007 Oct 31; 27(44):11807-19. PMID: 17978017.
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  57. Dugladze T, Vida I, Tort AB, Gross A, Otahal J, Heinemann U, Kopell NJ, Gloveli T. Impaired hippocampal rhythmogenesis in a mouse model of mesial temporal lobe epilepsy. Proc Natl Acad Sci U S A. 2007 Oct 30; 104(44):17530-5. PMID: 17954918.
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  58. Tort AB, Rotstein HG, Dugladze T, Gloveli T, Kopell NJ. On the formation of gamma-coherent cell assemblies by oriens lacunosum-moleculare interneurons in the hippocampus. Proc Natl Acad Sci U S A. 2007 Aug 14; 104(33):13490-5. PMID: 17679692.
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  59. Beshel J, Kopell N, Kay LM. Olfactory bulb gamma oscillations are enhanced with task demands. J Neurosci. 2007 Aug 1; 27(31):8358-65. PMID: 17670982.
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  60. Behn CG, Brown EN, Scammell TE, Kopell NJ. Mathematical model of network dynamics governing mouse sleep-wake behavior. J Neurophysiol. 2007 Jun; 97(6):3828-40. PMID: 17409167.
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  61. Pervouchine DD, Netoff TI, Rotstein HG, White JA, Cunningham MO, Whittington MA, Kopell NJ. Low-dimensional maps encoding dynamics in entorhinal cortex and hippocampus. Neural Comput. 2006 Nov; 18(11):2617-50. PMID: 16999573.
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  62. Rotstein HG, Oppermann T, White JA, Kopell N. 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 Dec; 21(3):271-92. PMID: 16927211.
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  63. Soto G, Kopell N, Sen K. Network architecture, receptive fields, and neuromodulation: computational and functional implications of cholinergic modulation in primary auditory cortex. J Neurophysiol. 2006 Dec; 96(6):2972-83. PMID: 16899641.
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  64. Cunningham MO, Pervouchine DD, Racca C, Kopell NJ, Davies CH, Jones RS, Traub RD, Whittington MA. Neuronal metabolism governs cortical network response state. Proc Natl Acad Sci U S A. 2006 Apr 4; 103(14):5597-601. PMID: 16565217.
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  65. Sivan E, Kopell N. Oscillations and slow patterning in the antennal lobe. J Comput Neurosci. 2006 Feb; 20(1):85-96. PMID: 16511657.
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  66. Kuznetsov AS, Kopell NJ, Wilson CJ. Transient high-frequency firing in a coupled-oscillator model of the mesencephalic dopaminergic neuron. J Neurophysiol. 2006 Feb; 95(2):932-47. PMID: 16207783.
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  67. Jones SR, Kopell N. Local network parameters can affect inter-network phase lags in central pattern generators. J Math Biol. 2006 Jan; 52(1):115-40. PMID: 16195924.
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  68. Gloveli T, Dugladze T, Rotstein HG, Traub RD, Monyer H, Heinemann U, Whittington MA, Kopell NJ. Orthogonal arrangement of rhythm-generating microcircuits in the hippocampus. Proc Natl Acad Sci U S A. 2005 Sep 13; 102(37):13295-300. PMID: 16141320.
    View in: PubMed
  69. Börgers C, Epstein S, Kopell NJ. Background gamma rhythmicity and attention in cortical local circuits: a computational study. Proc Natl Acad Sci U S A. 2005 May 10; 102(19):7002-7. PMID: 15870189.
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  70. Rotstein HG, Pervouchine DD, Acker CD, Gillies MJ, White JA, Buhl EH, Whittington MA, Kopell N. Slow and fast inhibition and an H-current interact to create a theta rhythm in a model of CA1 interneuron network. J Neurophysiol. 2005 Aug; 94(2):1509-18. PMID: 15857967.
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  71. Jensen O, Goel P, Kopell N, Pohja M, Hari R, Ermentrout B. On the human sensorimotor-cortex beta rhythm: sources and modeling. Neuroimage. 2005 Jun; 26(2):347-55. PMID: 15907295.
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  72. Kopell N. Does it have to be this complicated? Focus on "Single-column thalamocortical network model exhibiting gamma oscillations, spindles, and epileptogenic bursts". J Neurophysiol. 2005 Apr; 93(4):1829-30. PMID: 15774709.
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  73. Börgers C, Kopell N. Effects of noisy drive on rhythms in networks of excitatory and inhibitory neurons. Neural Comput. 2005 Mar; 17(3):557-608. PMID: 15802007.
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  74. Kunec S, Hasselmo ME, Kopell N. Encoding and retrieval in the CA3 region of the hippocampus: a model of theta-phase separation. J Neurophysiol. 2005 Jul; 94(1):70-82. PMID: 15728768.
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  75. Sivan E, Kopell N. Mechanism and circuitry for clustering and fine discrimination of odors in insects. Proc Natl Acad Sci U S A. 2004 Dec 21; 101(51):17861-6. PMID: 15590772.
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  76. Netoff TI, Banks MI, Dorval AD, Acker CD, Haas JS, Kopell N, White JA. Synchronization in hybrid neuronal networks of the hippocampal formation. J Neurophysiol. 2005 Mar; 93(3):1197-208. PMID: 15525802.
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  77. Kopell N, Ermentrout B. Chemical and electrical synapses perform complementary roles in the synchronization of interneuronal networks. Proc Natl Acad Sci U S A. 2004 Oct 26; 101(43):15482-7. PMID: 15489269.
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  78. Rubchinsky LL, Kopell N, Sigvardt KA. Modeling facilitation and inhibition of competing motor programs in basal ganglia subthalamic nucleus-pallidal circuits. Proc Natl Acad Sci U S A. 2003 Nov 25; 100(24):14427-32. PMID: 14612573.
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  79. Cunningham MO, Davies CH, Buhl EH, Kopell N, Whittington MA. Gamma oscillations induced by kainate receptor activation in the entorhinal cortex in vitro. J Neurosci. 2003 Oct 29; 23(30):9761-9. PMID: 14586003.
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  80. Sung NS, Gordon JI, Rose GD, Getzoff ED, Kron SJ, Mumford D, Onuchic JN, Scherer NF, Sumners DL, Kopell NJ. Science education. Educating future scientists. Science. 2003 Sep 12; 301(5639):1485. PMID: 12970550.
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  81. Pinto DJ, Jones SR, Kaper TJ, Kopell N. Analysis of state-dependent transitions in frequency and long-distance coordination in a model oscillatory cortical circuit. J Comput Neurosci. 2003 Sep-Oct; 15(2):283-98. PMID: 14512752.
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  82. McMillen D, Kopell N. Noise-stabilized long-distance synchronization in populations of model neurons. J Comput Neurosci. 2003 Sep-Oct; 15(2):143-57. PMID: 14512745.
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  83. Medvedev GS, Wilson CJ, Callaway JC, Kopell N. Dendritic synchrony and transient dynamics in a coupled oscillator model of the dopaminergic neuron. J Comput Neurosci. 2003 Jul-Aug; 15(1):53-69. PMID: 12843695.
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  84. Acker CD, Kopell N, White JA. Synchronization of strongly coupled excitatory neurons: relating network behavior to biophysics. J Comput Neurosci. 2003 Jul-Aug; 15(1):71-90. PMID: 12843696.
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  85. Jones SR, Mulloney B, Kaper TJ, Kopell N. Coordination of cellular pattern-generating circuits that control limb movements: the sources of stable differences in intersegmental phases. J Neurosci. 2003 Apr 15; 23(8):3457-68. PMID: 12716954.
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  86. Börgers C, Kopell N. Synchronization in networks of excitatory and inhibitory neurons with sparse, random connectivity. Neural Comput. 2003 Mar; 15(3):509-38. PMID: 12620157.
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  87. Olufsen MS, Whittington MA, Camperi M, Kopell N. New roles for the gamma rhythm: population tuning and preprocessing for the Beta rhythm. J Comput Neurosci. 2003 Jan-Feb; 14(1):33-54. PMID: 12435923.
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  88. McMillen D, Kopell N, Hasty J, Collins JJ. Synchronizing genetic relaxation oscillators by intercell signaling. Proc Natl Acad Sci U S A. 2002 Jan 22; 99(2):679-84. PMID: 11805323.
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  89. Traub RD, Kopell N, Bibbig A, Buhl EH, LeBeau FE, Whittington MA. Gap junctions between interneuron dendrites can enhance synchrony of gamma oscillations in distributed networks. J Neurosci. 2001 Dec 1; 21(23):9478-86. PMID: 11717382.
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  90. Fuchs EC, Doheny H, Faulkner H, Caputi A, Traub RD, Bibbig A, Kopell N, Whittington MA, Monyer H. Genetically altered AMPA-type glutamate receptor kinetics in interneurons disrupt long-range synchrony of gamma oscillation. Proc Natl Acad Sci U S A. 2001 Mar 13; 98(6):3571-6. PMID: 11248119.
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  91. Whittington MA, Traub RD, Kopell N, Ermentrout B, Buhl EH. Inhibition-based rhythms: experimental and mathematical observations on network dynamics. Int J Psychophysiol. 2000 Dec 1; 38(3):315-36. PMID: 11102670.
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  92. Jones SR, Pinto DJ, Kaper TJ, Kopell N. Alpha-frequency rhythms desynchronize over long cortical distances: a modeling study. J Comput Neurosci. 2000 Nov-Dec; 9(3):271-91. PMID: 11139043.
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  93. White JA, Banks MI, Pearce RA, Kopell NJ. Networks of interneurons with fast and slow gamma-aminobutyric acid type A (GABAA) kinetics provide substrate for mixed gamma-theta rhythm. Proc Natl Acad Sci U S A. 2000 Jul 5; 97(14):8128-33. PMID: 10869419.
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  94. Karbowski J, Kopell N. Multispikes and synchronization in a large neural network with temporal delays. Neural Comput. 2000 Jul; 12(7):1573-606. PMID: 10935919.
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  95. Chow CC, Kopell N. Dynamics of spiking neurons with electrical coupling. Neural Comput. 2000 Jul; 12(7):1643-78. PMID: 10935921.
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  96. Kopell N, Ermentrout GB, Whittington MA, Traub RD. Gamma rhythms and beta rhythms have different synchronization properties. Proc Natl Acad Sci U S A. 2000 Feb 15; 97(4):1867-72. PMID: 10677548.
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  97. Bose A, Kopell N, Terman D. Almost synchronous solutions for pairs of neurons coupled by excitation. Physica D. 2000; 140:69-94.
  98. Nadim F, Manor Y, Kopell N, Marder E. Synaptic depression creates a switch that controls the frequency of an oscillatory circuit. Proc Natl Acad Sci U S A. 1999 Jul 6; 96(14):8206-11. PMID: 10393973.
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  99. LoFaro T, Kopell N. Timing regulation in a network reduced from voltage-gated equations to a one-dimensional map. J Math Biol. 1999 Jun; 38(6):479-533. PMID: 10422266.
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  100. Manor Y, Nadim F, Epstein S, Ritt J, Marder E, Kopell N. Network oscillations generated by balancing graded asymmetric reciprocal inhibition in passive neurons. J Neurosci. 1999 Apr 1; 19(7):2765-79. PMID: 10087088.
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  101. Chow CC, White JA, Ritt J, Kopell N. Frequency control in synchronized networks of inhibitory neurons. J Comput Neurosci. 1998 Dec; 5(4):407-20. PMID: 9877022.
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  102. White JA, Chow CC, Ritt J, Soto-Treviño C, Kopell N. Synchronization and oscillatory dynamics in heterogeneous, mutually inhibited neurons. J Comput Neurosci. 1998 Mar; 5(1):5-16. PMID: 9580271.
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  103. Ermentrout GB, Kopell N. Fine structure of neural spiking and synchronization in the presence of conduction delays. Proc Natl Acad Sci U S A. 1998 Feb 3; 95(3):1259-64. PMID: 9448319.
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  104. Marder E, Kopell N, Sigvardt K. Neurons, networks and motor behavior, P.S.G. Stein, S. Grillner, A.I. Selverston, and D.G. Stuart, eds. How computation aids in understanding biological networks. MIT Press. Cambridge, MA. 1998; 139-50.
  105. Hayes M, Kaper T, Kopell N, Ono K. 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.
  106. Terman D, Bose A, Kopell N. Dynamics of two mutually coupled slow inhibitory neurons. Physica D. 1998; 117:241-75.
  107. Kopell N, Abbott L, Soto-Trevino C. On the behavior of a neural oscillator electrically coupled to a bistable element. Physica D. 1998; 121:367-95.
  108. Kopell N. Networks of neurons as dynamical systems: From geometry to biophysics. Quarterly Appl. Math. 1998; 56:707-18.
  109. Skinner FK, Kopell N, Mulloney B. How does the crayfish swimmeret system work? Insights from nearest-neighbor coupled oscillator models. J Comput Neurosci. 1997 Apr; 4(2):151-60. PMID: 9154521.
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  110. Weimann JM, Skiebe P, Heinzel HG, Soto C, Kopell N, Jorge-Rivera JC, Marder E. Modulation of oscillator interactions in the crab stomatogastric ganglion by crustacean cardioactive peptide. J Neurosci. 1997 Mar 1; 17(5):1748-60. PMID: 9030633.
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  111. Kopell N. The legacy of Norbert Wiener: A centennial symposium. Oscillating networks of neurons: Mathematics and function. American Mathematical Society. Providence. 1997.
  112. Terman D, Bose A, Kopell N. Functional reorganization in thalamocortical networks: transition between spindling and delta sleep rhythms. Proc Natl Acad Sci U S A. 1996 Dec 24; 93(26):15417-22. PMID: 8986826.
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  113. Soto-Treviño C, Kopell N, Watson D. Parabolic bursting revisited. J Math Biol. 1996 Nov; 35(1):114-28. PMID: 9002243.
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  114. Kopell N. Lectures in applied math. Global center manifolds and singularly perturbed equations. A brief guide to the literature. American Mathematical Society. Providence. 1996; 31:47-50.
  115. Jones C, Kaper T, Kopell N. Tracking invariant manifolds up to exponentially small errors. SIAM J. Math. Anal. 1996; 27:558-77.
  116. Kopell N. Handbook of brain theory and neural networks, M. Arbib, ed. Chains of coupled oscillators. MIT Press. Cambridge. 1995; 178-83.
  117. Kopell N, Landman M. Spatial structure of the focusing singularity of the nonlinear Schrodinger equation: A geometric analysis. SIAM J. Appl. Math. 1995; 55:1297-323.
  118. Somers D, Kopell N. Waves and synchrony in arrays of oscillators of relaxation and non-relaxation type. Physica D. 1995; 89:169-83.
  119. Kopell N, Somers D. Anti-phase solutions in relaxation oscillators coupled through excitatory interactions. J Math Biol. 1995; 33(3):261-80. PMID: 7897329.
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  120. Kopell N, LeMasson G. Rhythmogenesis, amplitude modulation, and multiplexing in a cortical architecture. Proc Natl Acad Sci U S A. 1994 Oct 25; 91(22):10586-90. PMID: 7937997.
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  121. Skinner FK, Kopell N, Marder E. Mechanisms for oscillation and frequency control in reciprocally inhibitory model neural networks. J Comput Neurosci. 1994 Jun; 1(1-2):69-87. PMID: 8792226.
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  122. Kopell N. Rhythms and clues: Mechanisms of self-organization in nature. 1993 University Lecture. Boston University. Boston MA. 1994.
  123. Jones C, Kopell N. Tracking invariant manifolds with differential forms in singularly perturbed equations. J. Diff. Equa. 1994; 108:64-88.
  124. Jones C, Kopell N. Tracking invariant manifolds with differential forms in singularly perturbed equations. J. Diff. Equa. 1994; 108:64-88.
  125. LoFaro T, Kopell N, Marder E, Hooper S. Subharmonic coordination in networks of neurons with slow conductances. Neural Computation. 1994; 6:69-84.
  126. Ermentrout GB, Kopell N. Inhibition-produced patterning in chains of coupled nonlinear oscillators. SIAM J. Appl. Math. 1994; 54:478-507.
  127. Ermentrout GB, Kopell N. Learning of phase-lags in coupled neural oscillators. Neural Computation. 1994; 6:225-41.
  128. Skinner F, Gramoll S, Calabrese R, Kopell N, Marder E. Computations in neurons and neural systems, F.H. Eeckman, ed. Frequency control in biological half-center oscillators. Kluwer. Boston. 1994; 223-8.
  129. LoFaro T, Kopell N, Marder E, Hooper S. Computations in neurons and neural systems, F.H. Eeckman, ed. The effect of i_h bursting patterns of pairs of coupled neurons. Kluwer. Boston. 1994; 15-20.
  130. Tin SK, Kopell N, Jones CKRT. Invariant manifolds and singularly perturbed boundary value problems. SIAM J. Num. Anal. 1994; 31:1558-76.
  131. Kopell N. From topology to computation: Proceedings of the Smalefest. Dynamical systems and the geometry of singularly perturbed equations. Springer-Verlag. New York. 1993.
  132. Marder E, Abbott L, Sharp A, Kopell N. From neural networks to artificial intelligence, Research notes in neural computing, M. Arbib, P. Rudomin, and F. Cervantes, eds. Electrical coupling in networks containing oscillators. Springer Verlag. New York. 1993; 33-42.
  133. Somers D, Kopell N. Rapid synchronization through fast threshold modulation. Biol Cybern. 1993; 68(5):393-407. PMID: 8476980.
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  134. Cohen AH, Ermentrout GB, Kiemel T, Kopell N, Sigvardt KA, Williams TL. Modelling of intersegmental coordination in the lamprey central pattern generator for locomotion. Trends Neurosci. 1992 Nov; 15(11):434-8. PMID: 1281350.
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  135. Ermentrout GB, Kopell N. Multiple pulse interactions and averaging in coupled neural oscillators. Journal of Math. Biol. 1991; 29:195-217.
  136. Kopell N, Ermentrout GB, Williams T. On chains of neural oscillators forced at one end. SIAM J. Appl. Math. 1991; 51:1397-17.
  137. Jones C, Kopell N, Langer R. Pattern and dynamics in reactive media, IMA Volumes in Mathematics and its Applications, H. Swinney, G. Aris and D. Aronson, eds. Construction of the FitzHugh-Nagumo pulse using differential forms. Springer-Verlag. New York. 1991; 37:101-16.
  138. Williams TL, Sigvardt KA, Kopell N, Ermentrout GB, Remler MP. Forcing of coupled nonlinear oscillators: studies of intersegmental coordination in the lamprey locomotor central pattern generator. J Neurophysiol. 1990 Sep; 64(3):862-71. PMID: 2230930.
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  139. Kopell N, Ermentrout GB. Computational neuroscience, E. Schwartz, ed. Structure and function in an oscillating neural network. MIT Press. Boston. 1990; 201-9.
  140. Ermentrout GB, Kopell N. SIAM J. Appl. Math. Oscillator death in systems of coupled neural oscillators. 1990; 50:125-46.
  141. Kopell N, Ermentrout GB. Phase transitions and other phenomena in chains ofoscillators. SIAM J. Appl. Math. 1990; 50:1014-52.
  142. Aronson DG, Ermentrout GB, Kopell N. Amplitude response of coupled Oscillators. Physica D. 1990; 41:403-49.
  143. Kopell N, Zhang W, Ermentrout GB. Multiple coupling in chains of oscillators. SIAM J. Math. Anal. 1990; 21:935-53.
  144. Ermentrout GB, Kopell N. Theoretical models of cell signalling, A. Goldbeter, ed. Some mathematical questions concerning central pattern generators. Academic Press. New York. 1989; 89-98.
  145. Kopell N, Ermentrout GB. Coupled oscillators and the design of central pattern generators. Math. Biosciences. 1988; 90:87-109.
  146. Kopell N. Dynamic patterns in complex systems, S. Kelso, ed. 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. World Scientific Publishers. 1988; 156-161.
  147. Kopell N. Neural control of rhythmic movements, A. Cohen, S. Grillner, S. Rossignol, eds. Toward a theory of modelling central pattern generators. J. Wiley. New York. 1987; 369-413.
  148. Ermentrout GB, Kopell N. Parabolic bursting in an excitable system coupled with a slow oscillation. SIAM J. Appl. Math. 1986; 46:233-53.
  149. Kopell N, Ermentrout GB. Subcellular oscillations and bursting. Math. Biosciences. 1986; 78:265-91.
  150. Kopell N, Ruelle D. Bounds on complexity in reaction-diffusion systems. SIAM J. Appl. Math. 1986; 46:68-80.
  151. N. Kopell. Phase methods for coupled oscillators and related topics: An annotated Bibliography. J. Statistical Physics. 1986; 44:1035-42.
  152. Kopell N. Nonlinear oscillations in biology and chemistry, H. Othmer, ed., Lecture Notes in Biomathematics. Coupled oscillators and locomotion by fish. Springer-Verlag. New York. 1986; 66:166-74.
  153. Kopell N . 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. Modelling C.P.G.'s: A robust approach. Macmillan. London. 1986; 383-5.
  154. Kopell N, Ermentrout GB. Symmetry and phaselocking in chains of weakly coupledOscillators. Comm. Pure Appl. Mathematics. 1986; 39:623-60.
  155. Kopell N. Invariant manifolds and the initialization problem for some atmospheric equations. Physica D. 1985; 14:203-15.
  156. Ermentrout GB, Kopell N. Frequency plateaus in a chain of weakly coupled Oscillators. SIAM J. on Math. Anal. 1984; 15:215-37.
  157. Kopell N. Proc. of the 1983 International Congress, Warsaw. Forced and coupled oscillators in biological applications. International Congress. North Holland, Amsterdam. 1984; 1645-60.
  158. Kopell N. Chaos in nonlinear dynamical systems, J. Chandra, ed. Symmetry and coherence in a chain of coupled oscillators. SIAM. Philadelphia. 1984; 86-93.
  159. Kopell N, Washburn R. Chaotic motions in the two-degree of freedom swing equations. IEEE Transactions on Circuits and Systems, Special Issue on Power Systems. 1982; CAS-29(11):738-46.
  160. Kopell N. Nonlinear Partial Differential Equations, Contemporary Mathematics, J. Smoller, ed. Frequency plateaus in a chain of weakly coupled oscillators. American Mathematical Society. Providence. 1982; 17:401-4.
  161. Kopell N, Ermentrout GB. Oscillation in mathematical biology, Lecture Notes in Biomathematics, J.P.E. Hodgson, ed. Coupled oscillators and mammalian small intestines. Springer-Verlag. New York. 1982; 51:24-36.
  162. Kopell N, Howard LN. 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.
  163. Kopell N, Parter S. A complete analysis of a model nonlinear equation having a continuous locus of turning points. Advances in Appl. Math. 1981; 2:212-38.
  164. Kopell N, Howard LN. Target patterns and spiral solutions to reaction-diffusion equations with more than one space dimension. Adv. Appl. Math. 1981; 2:417-49.
  165. Kopell N. Target pattern solutions to reaction-diffusion equations in the presence of impurities. Adv. Appl. Math. 1981; 2:389-99.
  166. Kopell N. Nonlinear dynamics, R. Helleman, ed. Time periodic but spatially irregular solutions to a model reaction-diffusion equation. Academy of Sciences. New York, NY. 1980; 397-409.
  167. Kopell, N. Singular perturbations and asymptotics, R. Meyer, ed. The singularly perturbed turning point problem: A geometric approach. Academic Press. New York. 1980; 173-90.
  168. Kopell N. A geometric approach to boundary layer problems exhibiting resonance. SIAM J. Appl. Math. 1979; 37:436-58.
  169. Howard LN, Kopell N. The Hopf Bifurcation and its Applications, Applied Mathematical Sciences, J. Marsden and M. McCracken, eds. Translation, with editorial comments, of E. Hopf's Abzeigung einer periodischen Losung von einer stationaren Losung eines Differentialsystems. Springer-Verlag. New York. 1978; 19:163-205.
  170. Kopell N. Psychology and biology of language and thought: Essays in honor of Eric Lenneberg, G. Miller, ed. Pattern formation in chemistry and biology: A mini-survey of mechanisms. Academic Press. New York. 1978; 65-85.
  171. Kopell N. Studies in mathematical biology, S. Levin, ed. MAA Studies in Mathematics. Reaction-diffusion equations and pattern formation. Mathematical Association of America. 1978; 15:191-205.
  172. Howard LN, Kopell N. Slowly varying waves and shocks in reaction-diffusion equations. Studies in Appl. Math. 1977; 56:95-145.
  173. Kopell N. Nonlinear Diffusion, Research Notes in Mathematics. Waves, shocks and target patterns in an oscillating chemical reagen. Pitman. 1977; 14:129-54.
  174. Kopell N, Howard LN. Bifurcations and trajectories joining critical points. Adv. in Math. 1975; 18:306-58.
  175. Kopell N, Stolzenberg G. Commentary on Bishop's talk. Historia Mathematica. 1975; 2:519-21.
  176. Kopell N, Howard LN. Pattern formation in the Belousov reaction. Lectures on Mathematics in the Life Sciences. 1974; 7:201-16.
  177. Howard LN, Kopell N. Mathematical Aspects of Chemical and Biochemical Problems and Quantum Chemistry. Wave trains, shock structures and transition layers in reaction-diffusion equations. American Mathematical Society. Providence. 1974; 8:274-83.
  178. Kopell N. Discussion paper: dissipative and nondissipative structure. Ann N Y Acad Sci. 1974; 231(1):106-7. PMID: 4522887.
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  179. Kopell N, Howard LN. Horizontal bands in the belousov reaction. Science. 1973 Jun 15; 180(4091):1171-3. PMID: 17743601.
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  180. Kopell N, Howard LN. Plane wave solutions to reaction diffusion equations. Studies in Appl. Math. 1973; 52:291-328.
  181. Kopell N. Global Analysis, Symposia in Pure Mathematics. Commuting diffeomorphisms. American Mathematical Society. Providence. 1970; 14:165-84.
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