TY - JOUR
T1 - Stationary pulses and wave front formation in an excitable medium
AU - Bountis, T.
AU - Starmer, C. F.
AU - Bezerianos, A.
N1 - Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.
PY - 2000
Y1 - 2000
N2 - 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.
AB - 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.
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U2 - 10.1143/PTPS.139.12
DO - 10.1143/PTPS.139.12
M3 - Article
AN - SCOPUS:0034393451
SP - 12
EP - 33
JO - Progress of Theoretical Physics Supplement
JF - Progress of Theoretical Physics Supplement
SN - 0375-9687
IS - 139
ER -