Copyright © 2009 Robert Artebrant. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

1. Y. Rudy and J. R. Silva, “Computational biology in the study of cardiac ion channels and cell electrophysiology,” Quarterly Reviews of Biophysics, vol. 39, no. 1, pp. 57–116, 2006. View at Publisher · View at Google Scholar · View at PubMed
2. R. A. FitzHugh, “Impulses and physiological states in theoretical models of nerve membrane,” Biophysical Journal, vol. 1, no. 6, pp. 445–466, 1961.
3. A. T. Winfree, “Electrical instability in cardiac muscle: phase singularities and rotors,” Journal of Theoretical Biology, vol. 138, no. 3, pp. 353–405, 1989. View at Publisher · View at Google Scholar · View at MathSciNet
4. J. Keener and J. Sneyd, Mathematical Physiology II: Systems Physiology, Springer, New York, NY, USA, 2008.
5. J. Sundnes, G. T. Lines, X. Cai, B. F. Nielsen, K.-A. Mardal, and A. Tveito, Computing the Electrical Activity in the Heart, Springer, New York, NY, USA, 2006.
6. J. Keener and J. Sneyd, Mathematical Physiology, Springer, New York, NY, USA, 2004.
7. A. Rabinovitch, I. Aviram, N. Gulko, and E. Ovsyshcher, “A model for the propagation of action potentials in non-uniformly excitable media,” Journal of Theoretical Biology, vol. 196, no. 2, pp. 141–154, 1999. View at Publisher · View at Google Scholar · View at PubMed
8. A. Rabinovitch, M. Gutman, Y. Biton, and I. Aviram, “Chaotic wave trains in an oscillatory/excitable medium,” Physics Letters A, vol. 360, no. 1, pp. 84–91, 2006. View at Publisher · View at Google Scholar
9. A. Pumir, A. Arutunyan, V. Krinsky, and N. Sarvazyan, “Genesis of ectopic waves: role of coupling, automaticity, and heterogeneity,” Biophysical Journal, vol. 89, no. 4, pp. 2332–2349, 2005. View at Publisher · View at Google Scholar · View at PubMed · View at Scopus
10. A. Tveito and G. T. Lines, “A condition for setting off ectopic waves in computational models of excitable cells,” Mathematical Biosciences, vol. 213, no. 2, pp. 141–150, 2008. View at Publisher · View at Google Scholar · View at PubMed · View at Zentralblatt MATH · View at MathSciNet
11. R. Artebrant, A. Tveito, and G. T. Lines, “A method for analyzing the stability of the resting state for a model of pacemaker cells surrounded by stable cells,” submitted to Mathematical Biosciences and Engineering.
12. H. Hayashi, C. Wang, Y. Miyauchi, et al., “Aging-related increase to inducible atrial fibrillation in the rat model,” Journal of Cardiovascular Electrophysiology, vol. 13, no. 8, pp. 801–808, 2002. View at Publisher · View at Google Scholar
13. G. Iooss and D. D. Joseph, Elementary Stability and Bifurcation Theory, Springer, New York, NY, USA, 1997.
14. J. Rinzel, “Repetitive activity and Hopf bifurcation under point stimulation for a simple FitzHugh-Nagumo nerve conduction model,” Journal of Mathematical Biology, vol. 5, no. 4, pp. 363–382, 1978. View at Zentralblatt MATH · View at MathSciNet
15. J. Rinzel and J. B. Keller, “Traveling wave solutions of a nerve conduction equation,” Biophysical Journal, vol. 13, no. 12, pp. 1313–1337, 1973. View at Publisher · View at Google Scholar
16. J. Rinzel and J. P. Keener, “Hopf bifurcation to repetitive activity in nerve,” SIAM Journal on Applied Mathematics, vol. 43, no. 4, pp. 907–922, 1983. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
17. D. H. Griffel, Applied Functional Analysis, Dover, Mineola, NY, USA, 2002.
18. D. E. Müller, “A method for solving algebraic equations using an automatic computer,” Mathematical Tables and Other Aids to Computation, vol. 10, no. 56, pp. 208–215, 1956. View at Publisher · View at Google Scholar · View at MathSciNet