Free access
Issue
ESAIM: M2AN
Volume 44, Number 6, November-December 2010
Page(s) 1225 - 1238
DOI http://dx.doi.org/10.1051/m2an/2010028
Published online 15 April 2010
  1. J. Carr, Applications of Centre Manifold Theory. Springer-Verlag, New York (1981).
  2. S. Dai and D.G. Schaeffer, Spectrum of a linearized amplitude equation for alternans in a cardiac fiber. SIAM J. Appl. Math. 69 (2008) 704–719. [CrossRef] [MathSciNet]
  3. B. Echebarria and A. Karma, Instability and spatiotemporal dynamics of alternans in paced cardiac tissue. Phys. Rev. Lett. 88 (2002) 208101. [CrossRef] [PubMed]
  4. B. Echebarria and A. Karma, Amplitude-equation approach to spatiotemporal dynamics of cardiac alternans. Phys. Rev. E 76 (2007) 051911. [CrossRef] [MathSciNet]
  5. A. Garfinkel, Y.-H. Kim, O. Voroshilovsky, Z. Qu, J.R. Kil, M.-H. Lee, H.S. Karagueuzian, J.N. Weiss and P.-S. Chen, Preventing ventricular fibrillation by flattening cardiac restitution. Proc. Natl. Acad. Sci. USA 97 (2000) 6061–6066. [CrossRef]
  6. R.F. Gilmour Jr. and D.R. Chialvo, Electrical restitution, Critical mass, and the riddle of fibrillation. J. Cardiovasc. Electrophysiol. 10 (1999) 1087–1089. [CrossRef] [PubMed]
  7. M. Golubitsky and D.G. Schaeffer, Singularities and Groups in Bifurcation Theory. Springer-Verlag, New York (1985).
  8. J. Guckenheimer, On a codimension two bifurcation, in Dynamical Systems and Turbulence, Warwick 1980, Lect. Notes in Mathematics 898, Springer (1981) 99–142.
  9. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dyanamical Systems, and Bifurcations of Vector Fields. Springer-Verlag, New York (1983).
  10. M.R. Guevara, G. Ward, A. Shrier and L. Glass, Electrical alternans and period doubling bifurcations, in Proceedings of the 11th Computers in Cardiology Conference, IEEE Computer Society, Los Angeles, USA (1984) 167–170.
  11. P. Holmes, Unfolding a degenerate nonlinear oscillator: a codimension two bifurcation, in Nonlinear Dynamics, R.H.G. Helleman Ed., New York Academy of Sciences, New York (1980) 473–488.
  12. W.F. Langford, Periodic and steady state interactions lead to tori. SIAM J. Appl. Math. 37 (1979) 22–48. [CrossRef] [MathSciNet]
  13. C.C. Mitchell and D.G. Schaeffer, A two-current model for the dynamics of the cardiac membrane. Bull. Math. Biol. 65 (2003) 767–793. [CrossRef] [PubMed]
  14. D. Noble, A modification of the Hodgkin-Huxley equations applicable to Purkinje fiber actoin and pacemaker potential. J. Physiol. 160 (1962) 317–352. [PubMed]
  15. J.B. Nolasco and R.W. Dahlen, A graphic method for the study of alternation in cardiac action potentials. J. Appl. Physiol. 25 (1968) 191–196. [CrossRef] [PubMed]
  16. A.V. Panfilov, Spiral breakup as a model of ventricular fibrillation. Chaos 8 (1998) 57–64. [CrossRef] [MathSciNet] [PubMed]

Recommended for you