Publications


  1. ``Bernstein-Gelfand-Gelfand Reciprocity on Perverse Sheaves.'' Annales Scientifiques de l'Ecole Normale Superieure 4e Serie 20 (1987): 311-323 (with K.~Vilonen) pdf
     
  2. ``Phase Locking and Critical Phenomena in Lattices of Coupled Nonlinear Oscillators with Random Intrinsic Frequencies.'' Physica D 31 (1988): 143-168 (with S.~Strogatz) pdf
     
  3. ``Collective Synchronization in Lattices of Nonlinear Oscillators with Randomness.'' Journal of Physics A: Mathematical and General 21 (1988): L699-L705 (with S.~Strogatz) pdf
     
  4. ``Simple Model of Collective Transport with Phase Slippage.'' Physical Review Letters 61 (1988): 2380-2383 (with C.~M.~Marcus, S.~Strogatz and R.~M.~Westervelt) pdf
     
  5. ``Collective Dynamics of Coupled Oscillators with Random Pinning.'' Physica D 36 (1989): 23-50 (with C.~M.~Marcus, S.~Strogatz and R.~M.~Westervelt) pdf
     
  6. ``Jump Bifurcation and Hysteresis in an Infinite-Dimensional Dynamical System of Coupled Spins.'' SIAM Journal on Applied Mathematics 50 (1990): 108-124 (with S.~Strogatz) pdf
     
  7. ``Amplitude Death in an Array of Limit Cycle Oscillators.'' Journal of Statistical Physics 60 (1990): 245-262 (with S.~Strogatz) pdf
     
  8. ``Integral Representation of a Finite Spike.'' American Mathematical Monthly 97 (1990): 901-903 (with S.Strogatz) pdf
     
  9. ``Synchronization of Pulse Coupled Biological Oscillators.'' SIAM Journal on Applied Mathematics 50 (1990): 1645-1662 (with S.~Strogatz) pdf
     
  10. ``Dynamics of a Globally Coupled Oscillator Array.'' Physica D 48 (1991): 102-112 (with K.~Tsang, S.~Strogatz, K.~Wiesenfeld) pdf
     
  11. ``Stability of Incoherence in a Population of Coupled Oscillators.'' Journal of Statistical Physics 63 (1991): 613-635 (with S.~Strogatz) pdf
     
  12. ``Dynamics of a Large System of Coupled Nonlinear Oscillators.'' Physica D 52 (1991): 293-331 (with P.~Matthews, S.~Strogatz) pdf
     
  13. ``Reversibility and Noise Sensitivity of Josephson Arrays.'' Phys. Rev. Lett. 6 (1991): 1094-1097 (with K.~Tsang, S.~Strogatz, and K.~Wiesenfeld) pdf
     
  14. ``Coupled Nonlinear Oscillators below the Synchronization Threshold: Relaxation by Generalized Landau Damping.'' Physical Review Letters 68 (1992): 2730-2733 (with P.~Matthews and S.~Strogatz) pdf
     
  15. ``Splay States in Globally Coupled Josephson Arrays: Analytical Prediction of Floquet Multipliers.'' Physical Review E 47 (1993): 220-227 (with S.~Strogatz) pdf
     
  16. ``Splay Phase Orbits for Equivariant Flows on Tori.'' SIAM Journal on Mathematical Analysis 25 (1994): 1176-1180 pdf
     
  17. ``Existence, Uniqueness and Non-uniqueness of Single-Wave-Form Solutions to Josephson Junction Systems.'' SIAM Journal on Applied Mathematics 60 (2000): 1471-1501 (with N.~Rosen) pdf
     
  18. ``The Spectrum of the Locked State for the Kuramoto Model of Coupled Oscillators.'' Physica D 205 (2005): 249-266 (with S. Strogatz) pdf
     
  19. ``The Spectrum of the Partially Locked State for the Kuramoto Model.'' Journal of Nonlinear Science 17 (2007): 309-347 (with S.~Strogatz) pdf
     
  20. ``Solvable Model For Chimera States Of Coupled Oscillators.'' Physical Review Letters 101, 084103 (2008) (with D.~Abrams and S.~Strogatz) pdf
     
  21. ``Dynamical Phase Transitions In Periodically Driven Model Neurons.'' Physical Review E 79, 021904 (2009) (with J.~R.~Engelbrecht) pdf
     
  22. ``Identical Phase Oscillators With Global Sinusoidal Coupling Evolve By M\"obius Group Actions.'' Chaos 19, 043104 (2009) (with S.~Marvel and S.~Strogatz) pdf
     
  23. ``The Structure Of Long-term Average Frequencies For Kuramoto Oscillator Systems.'' Physical Review Letters 109 (3), 034103 (2012) (with J.~R.~Engelbrecht) pdf
     
  24. ``Rhythm-Induced Spike-Timing Patterns Characterized by 1D Firing Maps.'' Journal Of Computational Neuroscience 10.1007/s10827-012-0406-8 (2012) (with J.~R.~Engelbrecht) pdf
     
  25. ``The Asymptotic Behavior Of The Order Parameter For The Infinite-N Kuramoto Model.'' Chaos 22, 043118 (2012) pdf
     
  26. ``Classification Of Attractors For Coupled Identical Kuramoto Oscillator Networks." Chaos 24, 013114 (2014) (with J.~R.~Engelbrecht) pdf