A simple scalar coupled map lattice model for excitable media

Book English OPEN
Guo, Y. ; Zhao, Y. ; Coca, D. ; Billings, S.A. (2010)
  • Publisher: Automatic Control and Systems Engineering, University of Sheffield

A simple scalar coupled map lattice model for excitable media is intensively analysed in this paper. This model is used to explain the excitability of excitable media, and a Hopf-like bifurcation is employed to study the different spatio-temporal patterns produced by the model. Several basic rules for the construction of these kinds of models are proposed. Illustrative examples demonstrate that the sCML model is capable of generating complex spatiotemporal patterns.
  • References (20)
    20 references, page 1 of 2

    Barkley, D. [1991]. "A model for fast computer-simulation of waves in excitable media." Physica D, 49, 61-70.

    Billings, S. A., &Coca, D. [2002]. "Identification of coupled map lattice models of deterministic distributed parameter systems." International Journal of Systems Science, 33, 623-634.

    Chua, L. O. [2007]. A Nonlinear Dynamics Perspective of Wolfram's New Kind of Science, (World Scientific Publishing Co., Inc.).

    Chua, L. O., &Yang, L. [1988]. "Cellular neural networks: Theory." IEEE transactions on circuits and systems, 35, 1257-1272.

    Coca, D., &Billings, S. A. [2001]. "Identification of coupled map lattice models of complex spatio-temporal patterns." Physics Letters, Section A: General, Atomic and Solid State Physics, 20 287, 65-73.

    Difrancesco, D., &Noble, D. [1985]. "A model of cardiac electrical activity incorporating ionic pumps and concentration changes." Philosophical Transactions of the Royal Society of London Series B-Biological Sciences, 307, 353-398.

    Field, R. J., Noyes, R. M., &Koros, E. [1972]. "Oscillations in chemical systems 2. through analysis of temporal oscillation in bromate-cerium-malonic acid systems." Journal of the American Chemical Society, 94, 8649-64.

    FitzHugh, R. [1955]. "Mathematical models of threshold phenomena in the nerve membrane." Bulletin of Mathematical Biology, 17, 257-278.

    Fortuna, L., Arena, P., Bálya, D., &Zarándy, Á. [2001]. "Cellular Neural Networks: A Paradigm for Nonlinear Spatio-Temporal Processing." IEEE Circuits and Systems Magazine, 1, 6-21.

    Gerhardt, M., Schuster, H., &Tyson, J. J. [1990]. "A cellular automaton model of excitable media including curvature and dispersion." Science, 247, 1563-1566.

  • Metrics
    0
    views in OpenAIRE
    0
    views in local repository
    29
    downloads in local repository

    The information is available from the following content providers:

    From Number Of Views Number Of Downloads
    White Rose Research Online - IRUS-UK 0 29
Share - Bookmark