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Stationary pulses and wave front formation in an excitable medium

Publication ,  Journal Article
Bountis, T; Starmer, CF; Bezerianos, A
Published in: Progress of Theoretical Physics Supplement
January 1, 2000

In an excitable medium, the method of phase plane analysis of ODE reductions is often used to separate suprathreshold disturbances that collapse from disturbances that expand and result in a propagating front. Following this approach, we study here pulse formation in 1-Dimensional (1-D) and 2-D media and derive closed form (1-D) and approximate (2-D) expressions for a critical pulse structure, which is stationary but unstable. This critical structure, called a stationary pulse, can be modulated by altering (e.g. adding a constant to) the reaction portion of the reaction-diffusion equation, suggesting a mechanism for extinguishing the initial expanding phase of front formation or for steering a front. We have also studied analytically and numerically the onset of "recovery", leading from a single wavefront to an ordinary action potential wave. Possible applications of these ideas to the development of practical strategies for controlling cardiac arrhythmia are discussed.

Duke Scholars

Published In

Progress of Theoretical Physics Supplement

DOI

ISSN

0375-9687

Publication Date

January 1, 2000

Issue

139

Start / End Page

12 / 33

Related Subject Headings

  • Nuclear & Particles Physics
  • 02 Physical Sciences
  • 01 Mathematical Sciences
 

Citation

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Bountis, T., Starmer, C. F., & Bezerianos, A. (2000). Stationary pulses and wave front formation in an excitable medium. Progress of Theoretical Physics Supplement, (139), 12–33. https://doi.org/10.1143/PTPS.139.12
Bountis, T., C. F. Starmer, and A. Bezerianos. “Stationary pulses and wave front formation in an excitable medium.” Progress of Theoretical Physics Supplement, no. 139 (January 1, 2000): 12–33. https://doi.org/10.1143/PTPS.139.12.
Bountis T, Starmer CF, Bezerianos A. Stationary pulses and wave front formation in an excitable medium. Progress of Theoretical Physics Supplement. 2000 Jan 1;(139):12–33.
Bountis, T., et al. “Stationary pulses and wave front formation in an excitable medium.” Progress of Theoretical Physics Supplement, no. 139, Jan. 2000, pp. 12–33. Scopus, doi:10.1143/PTPS.139.12.
Bountis T, Starmer CF, Bezerianos A. Stationary pulses and wave front formation in an excitable medium. Progress of Theoretical Physics Supplement. 2000 Jan 1;(139):12–33.

Published In

Progress of Theoretical Physics Supplement

DOI

ISSN

0375-9687

Publication Date

January 1, 2000

Issue

139

Start / End Page

12 / 33

Related Subject Headings

  • Nuclear & Particles Physics
  • 02 Physical Sciences
  • 01 Mathematical Sciences