Selected Publications
Bifurcations and singularly perturbed equations.
- N. Kopell and L.N. Howard. Bifurcation under non-generic conditions. Adv. in Math., 1974;13:274-83.
- * N. Kopell and L.N. Howard. Bifurcations and trajectories joining critical points. Adv. in Math., 1975;18:306-58.
- * N. Kopell. A geometric approach to boundary layer problems exhibiting resonance. SIAM J. Appl. Math, 1979;37:436-58.
- 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.
- C. Jones, N. Kopell, and R. Langer. Construction of the FitzHugh-Nagumo pulse using differential forms. Patterns 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;37:101-115.
- D. Somers and N. Kopell. Rapid synchronization through fast threshold modulation. Biol.Cybern., 1993;68:393-407.
- * C. Jones and N. Kopell. Tracking invariant manifolds with differential forms in singularly perturbed equations. J. Diff. Equa., 1994;108:64-88.
- 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 and D. Somers. Anti-phase solutions in relaxation oscillators coupled through excitatory interactions. J. Math. Biol., 1995;33:261-8.
- * 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.
- 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.
- * 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.
- H. Rotstein, N. Kopell, A. Zhabotinsky, and I. Epstein. A canard mechanism in systems of globally coupled oscillators. SIAM J. Appl. Math., 2003;63:1998-2019.
- H. Rotstein, N. Kopell, A. Zhabotinsky, and I. Epstein. Canard phenomenon and localization of oscillations in the Belousov-Zhabotinsky reaction with global feedback. J. Chemical Physics, 2003;119:8824-32.
- A. Kuznetsov, M. Kaern, and N. Kopell. Synchrony in a population of hysteresis-based genetic oscillators. SIAM J. Appl. Math., 2004; 65:392-425.
- 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.
- 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.
- M. Kramer, R. Traub, and N. Kopell. New dynamics in cerebellar Purkinje cells: torus canards. Physical review letters, 2008 Aug 8;101(6):068103. doi: 10.1103/PhysRevLett.101.068103 Epub 2008 Aug 8.
- J. Mitry, M. McCarthy, N. Kopell, and M. Wechselberger. Excitable neurons, firing threshold manifolds and canards. J. Math. Neurosci., 2013 3:12 (14 August 2013, online).
- 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.
- J. Cannon and N. Kopell. The Leaky Oscillator: Properties of Inhibition-Based Rhythms Revealed through the Singular Phase Response Curve. SIAM J. Applied Dynamical Systems 2015 Society for Industrial and Applied Mathematics, Vol. 14, No. 4, pp. 1930–1977.