Skip to main content
Log in

On Difference Equations Motivated by Modelling the Heart

  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

The analytical structure of some generalizations of the circle map is given. Also a generalization of off centre reflection is studied. The stability of Ito-Glass coupled map lattice is studied.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Ahmed, E. and Hegazi, A. S., ‘On persistence and stability of somespatially inhomogeneous systems’, Journal of Mathematical Analysis and Applications 268, 2002, 74–88.

    Article  MATH  MathSciNet  Google Scholar 

  2. Au, T. K. -K., ‘The dynamics of off centre reflections’, Journal of Mathematical Analysis and Applications 264, 2001, 311–323.

    Article  MATH  MathSciNet  Google Scholar 

  3. Belair, J. and Glass, L., ‘Universality and self similarity in the bifurcation of circle maps’, Physica 16D, 1985, 143–154.

    MathSciNet  ADS  Google Scholar 

  4. Boyland, P. L., ‘Bifurcations of circle maps’, Communications in Mathematical Physics 106, 1986, 353–381.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  5. Bub, G. and Glass, L., ‘Bifurcations in a discontinuous circle map’, International Journal of Bifurcation and Chaos 5, 1995, 359–371.

    Article  MATH  MathSciNet  Google Scholar 

  6. Courtemanche, M., Glass, L., Belair, J., Scagliotti, D., and Gordon, D., ‘ A circle map in a human heart’, Physica D40, 1989, 299.

    MathSciNet  ADS  Google Scholar 

  7. Holmgren, R., Introduction to Discrete Dynamical Systems, Springer, Berlin, 1996.

    Google Scholar 

  8. Ito, R., ‘Rotation sets are closed’, Mathematical Proceedings of the Cambridge Philosophical Society 89, 1981, 107–111.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  9. Ito, H. and Glass, L., ‘Theory of reentrant excitation in a ring of cardiac tissue’, Physica 56D, 1992, 841.

    Google Scholar 

  10. Keener, J. P., ‘Chaotic behaviour in piecewise continuous difference equations’, Transactions of the American Mathematical Society 261, 1980, 589–605.

    Article  MATH  MathSciNet  Google Scholar 

  11. Murray, J. D., Mathematical Biology, Springer Publishers, Berlin, 2002.

    MATH  Google Scholar 

  12. Vandermeer, J., Stone, L., and Blasius, B., ‘Categories of choos and fractal basin boundaries in forced predator–prey models’,Chaos Solitons and Fractals 12 2001, 265.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. S. Elgazzar.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ahmed, E., Hegazi, A.S. & Elgazzar, A.S. On Difference Equations Motivated by Modelling the Heart. Nonlinear Dyn 46, 49–60 (2006). https://doi.org/10.1007/s11071-005-9006-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-005-9006-8

Keywords

Navigation