Synchronization of Nonlinear Oscillations and Circle Maps

  • L. Glass,, M.C. Mackey. A simple model for phase locking of biological oscillators. Journal of Mathematical Biology 7, 339-352 (1979). pdf file
  • L. Glass, C. Graves, G.A. Petrillo, M.C. Mackey. Unstable dynamics of a periodically driven oscillator in the presence of noise. Journal of Theoretical Biology 86, 455-475 (1980). pdf file
  • M.R. Guevara, L. Glass, A. Shrier. Phase locking, perioddoubling bifurcations and irregular dynamics in periodically stimulated cardiac cells. Science 214, 1350-1353 (1981).

  • M.R. Guevara, L. Glass. Phase locking, period doubling bifurcations and chaos in a mathematical model of a periodically driven biological oscillator: A theory for the entrainment of biological oscillators and the generation of cardiac dysrhythmias. Journal of Mathematical Biology 14, 1-23 (1982).

  • L. Glass, R. Perez. Fine structure of phase locking. Physical Review Letters 48, 1772-1775 (1982).pdf file

  • R. Perez, L. Glass. Bistability, period doubling bifurcations and chaos in a periodically forced oscillator. Physics Letters 90A, 441-443 (1982). pdf file

  • J. Bélair, L. Glass. Self similarity in periodically forced oscillators. Physics Letters 96A, 113-116 (1983). pdf file

  • G.A. Petrillo, L. Glass, T. Trippenbach. Phase locking of the respiratory rhythm in cats to a mechanical ventilator. Canadian Journal of Physiology and Pharmacology 61, 599-607 (1983).

  • M.R. Guevara, L. Glass, M.C. Mackey, A. Shrier. Chaos in neurobiology. Transactions of the IEEE, Systems, Man and Cybernetics, SMC13, 790-798 (1983).

  • L. Glass, M.R. Guevara, A. Shrier, R. Perez. Bifurcation and chaos in a periodically stimulated cardiac oscillator. Physica 7D, 89-101(1983). pdf file

  • J. Keener, L. Glass. Global bifurcations of a periodically forced nonlinear oscillator. Journal of Mathematical Biology 21, 175-190 (1984).

  • L. Glass, M.R. Guevara, J. Bélair, A. Shrier. Global bifurcations of a periodically forced biological oscillator. Physical Review A 29, 1348-1357 (1984). pdf file

  • G.A. Petrillo, L. Glass. A theory for phase locking of respiration in cats to a mechanical ventilator. American Journal of Physiology 246, (Regulatory, Integrative Comprehensive Physiology 15), R311-R320 (1984). pdf file

  • J. Bélair, L. Glass. Universality and selfsimilarity in the bifurcations of circle maps. Physica 16D, 143-154 (1985). pdf file

  • C. Graves, L. Glass, D. Laporta, R. Meloche, A. Grassino. Respiratory phase locking during mechanical ventilation in anesthetized human subjects. American Journal of Physiology 250 (Regulatory, Integrative Comprehensive Physiology 19), R902-R909 (1986). pdf file

  • L. Glass, A. Goldberger, M. Courtemanche, A. Shrier. Nonlinear dynamics, chaos and complex cardiac arrhythmias. Proceedings of the Royal Society (London) A 413, 9-26 (1987). pdf file

  • J. Lewis, M. Bachoo, L. Glass, C. Polosa. Complex dynamics resulting from repeated stimulation of nonlinear oscillators at a fixed phase. Physics Letters 125 A, 119-122 (1987). pdf file

  • M.R. Guevara, A. Shrier, L. Glass. Phase-locked rhythms in periodically stimulated heart cell aggregates. American Journal of Physiology 254 (Heart Circ. Physiol. 23), H1-H10 (1988). pdf file

  • M. Courtemanche, L. Glass, M.D. Rosengarten, A.L. Goldberger. Beyond parasystole: Promises and problems in modelling complex arrhythmias. American Journal of Physiology 257 (Heart Circ. Physiol. 26), H693-H706 (1989). pdf file

  • D. Gordon, D. Scagliotti, M. Courtemanche, L. Glass. A clinical study of the dynamics of parasystole. PACE 12, 1412-1418 (1989).

  • W.Z. Zeng, L. Glass. Symbolic dynamics and skeletons of circle maps. Physica 40D, 218-234 (1989). pdf file

  • M. Courtemanche, L. Glass, J. Bélair, D. Scagliotti, D. Gordon. A circle map in a human heart. Physica 40D, 299-310 (1989). pdf file

  • W.Z. Zeng, M. Courtemanche, L. Sehn, A. Shrier, L. Glass. Theoretical computation of phase locking in embryonic atrial heart cell aggregates. Journal of Theoretical Biology 145, 225-244 (1990).

  • J. Lewis, M. Bachoo, C. Polosa, L. Glass. The effects of superior laryngeal nerve stimulation on the respiratory rhythm: phase resetting and aftereffects. Brain Research 517, 44-50 (1990).

  • W.Z. Zeng, J. Morissette, R. Brochu, L. Glass, A. Shrier. Complex rhythms resulting from overdrive suppression in electrically stimulated cardiac pacemakers. PACE 13, 1678-1685 (1990).

  • L. Glass. Circle maps and cardiac arrhythmias A classical problem. Chaos: An Interdisciplinary Journal of Nonlinear Science 1, 13-19 (1991).

  • W.Z. Zeng, L. Glass, A. Shrier. Evolution of rhythms during periodic stimulation of embryonic chick heart cell aggregates. Circulation Research 69, 1022-1033 (1991).

  • W.Z. Zeng, L. Glass, A. Shrier. The topology of phase response curves induced by single and paired stimuli. Journal of Biological Rhythms 7, 89-104 (1992).

  • J. E. Lewis, L. Glass, M. Bachoo, C. Polosa. Phase resetting and fixed delay stimulation of a simple model of respiratory rhythm generation. Journal of Theoretical Biology 159, 491-506 (1992).

  • V.C. Kowtha, A. Kunysz, J.R. Clay, L, Glass, A. Shrier. Ionic mechanisms and nonlinear dynamics of embryonic chick heart cell aggregates. Progress in Biophysics and Molecular Biology 61, 255-281 (1994).

  • L. Glass, W. Zeng. Bifurcations in flat-topped maps and the control of cardiac chaos. International Journal of Bifurcation and Chaos 4, 1061-1067 (1994).

  • L. Glass, J. Sun. Periodic forcing of a limit cycle oscillator: Fixed points, Arnold tongues, and the global organization of bifurcations. Physical Review E 50, 5077-5084 (1994). pdf file

  • A. Kunysz, L. Glass, A. Shrier. Overdrive suppression of spontaneously beating chick heart cell aggregates: Experiment and theory. Am. J. Physiol. 269, H1153-H1164 (1995). pdf file

  • G. Bub, L. Glass. Bifurcations in a discontinuous circle map: A theory for a chaotic cardiac arrhythmia. International Journal of Bifurcation and Chaos 5, 359-371 (1995).

  • J. Sun, F. Amellal, L. Glass, J. Billette. Alternans and period doubling bifurcations in atrioventricular nodal conduction. Journal of Theoretical Biology 173, 79-91 (1995). pdf file

  • T. Nomura, L. Glass. Entrainment and termination of reentrant wave propagation in a periodically stimulated ring of excitable media. Physical Review E 53, 6353-6360 (1996). pdf file

  • D.T. Kaplan, J.R. Clay, T. Manning, L. Glass, M.R. Guevara, A. Shrier. Subthreshold dynamics in periodically stimulated squid giant axons. Physical Review Letters 76, 4074-4077 (1996). pdf file

  • L. Glass. Synchronization and rhythmic processes in physiology. Nature, 410, 277-284 (2001) (Insight review article). pdf file

  • L. Glass, Y. Nagai, K. Hall, M. Talajic, S. Nattel. Predicting the entrainment of reentrant cardiac waves using phase resetting curves. Physical Review E, 65, 021908 (2002). pdf file

  • P. Jorgensen, C. Schafer, P. G. Guerra, M. Talajic, S. Nattel, L. Glass. A mathematical model of human atrioventricular nodal function incorporating concealed conduction. Bulletin of Mathematical Biology 64, 1083-1099 (2002). pdf file

  • V. Schulte-Frohlinde, Y. Ashkenazy, A. L. Goldberger, P. Ch. Ivanov, M. Costa, A. Morley-Davies, H. E. Stanley, L. Glass. Complex patterns of abnormal heartbeats. Physical Review E, 66, 031901 (2002). pdf file

  • P. Martineau, M. Aguilar, L. Glass. Predicting perception of the wagon wheel illusion. Physical Review Letters, 103:2 (2009). pdf file