Stationary pulses and wave front formation in an excitable medium

In an excitable medium, the method of phase plane analysis of ODE reduction s 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 medi a and derive closed form (1-D) and approximate (2-D) expressions for a crit ical pulse structure, which is stationary but unstable. This critical struc ture, called a stationary pulse, can be modulated by altering (e.g. adding a constant to) the reaction portion of the reaction-diffusion equation, sug gesting a mechanism for extinguishing the initial expanding phase of front formation or for steering a front. We have also studied analytically and nu merically the onset of "recovery", leading from a single wavefront to an or dinary action potential wave. Possible applications of these ideas to the d evelopment of practical strategies for controlling cardiac arrhythmia are d iscussed.